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What is the hypotenuse and perimeter of a right angle triangle when its sides are in the ratio of 15 to 8 having an area of 297.0375 square cm showing all work?
Wiki User
∙ 10y ago
1 Let the sides be 15x and 8x
2 So: 0.5*15x*8x = 297.0375 => 120x2 = 594.075
3 Divide both sides by 120 and then square root both sides
4 Then: x = 2.225 so sides are 15*2.225 = 33.375 cm and 8*2.225 = 17.8 cm
5 Hypotenuse: 17*2.225 = 37.825 cm because its part of a Pythagorean triple
6 Perimeter: 37.825+33.375+17.8 = 89 cm
7 Check: 0.5*33.375*17.8 = 297.0375 square cm
Wiki User
∙ 10y ago
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What is the hypotenuse and perimeter of a right angle triangle when one side is 14 cm greater than the other side with an area of 240 square cm showing work?
1 Let the sides be x+14 and x 2 So: 0.5*(x+14)*x = 240 which transposes to x2+14x-480 3 Solving the above quadratic equation gives x a positive value of 16 4 Therefore the sides are 30 and 16 5 Using Pythagoras: 302+162 = 1156 and its square root is 34 6 Hypotenuse = 34 cm 7 Perimeter = 34+30+16 = 80 cm
What is the perimeter of a right angle triangle whose hypotenuse is 17 cm when one side is shorter than the other side by 7 cm showing work?
Let the sides be x and x-7 So using Pythagoras: x2+(x-7)2 = 172 => 2x2-14x-240 = 0 Solving the quadratic equation gives x a positive value of 15 Therefore sides are: 15 and 15-7 = 8 Perimeter: 17+15+8 = 40 cm
What is the perimeter of an isosceles triangle whose base is 15.96 cm with an area of 84.9072 square cm showing all work and answer?
These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.
Can you work out the length of the hypotenuse of a right angle triangle with sides VIII and VI inches showing all your workings in roman numerals?
Pythagoras' Theorem states that for any right angle triangle the height squared plus the base squared is equal to the square of the hypotenuse. In other words, after finding the square of the hypotenuse, square root your answer to find its length. Hence: (8*8)+(6*6)=64+36=100. The square root of 100=10. Therefore the length of the hypotenuse is 10 inches. In Roman numerals: (VIII*VIII)+(VI*VI)=LXIIII+XXXVI=C. The square root of C=X. Therefore the length of the hypotenuse is X inches. David Gambell, Merseyside, England.
What is the perimeter of a right angle triangle that has an hypotenuse of 20.8 cm and an area of 76.8 square cm showing work?
Square 20.8 and square (2*76.8) then find two numbers which have been squared that have a sum of 432.64 and a product of 23592.96 Let the squared numbers be x and y:- If: x+y = 432.64 Then: y = 432.64 -x If: xy = 23592.96 Then: x(432.64 -x) = 23592.96 So: 432.64x -x^2 -23592.96 = 0 Solving the above quadratic equation: x = 368.64 or x = 64 meaning y = 64 Square root of 368.64 = 19.2 and square root of 64 = 8 are sides of the triangle Therefore perimeter: 20.8+19.2+8 = 48 cm Check: 0.5*19.2*8 = 76.8 square cm Check: 19.2^2 + 8^2 = 432.64 and its square root is 20.8 which is the hypotenuse
What is the hypotenuse and perimeter of a right angle triangle whose sides are in the ratio of 3 to 4 with an area of 18.375 square cm showing all work?
Let its sides be 3x and 4x If: 0.5*3x*4x = 18.375 Then: 12x^2 = 36.75 => x^2 = 3.0625 => x = 1.75 So sides are: 5.25 cm and 7 cm Using Pythagoras its hypotenuse is: 8.75 cm Perimeter: 5.25+7+8.75 = 21 cm
What is the hypotenuse and perimeter of a right angle triangle whose sides are in the ratio of 5 to 12 with an area of 91.875 square cm showing all work?
1 Let the sides be 5x and 12x 2 So: 0.5*5x*12x = 91.875 and then 60x2 = 183.75 3 Divide both sides by 60 and then square root both sides 4 Therefore x = 1.75 and sides are 5*1.75 = 8.75 and 12*1.75 = 21 5 Using Pythagoras: 8.752+212 = 517.5625 and its square root is 22.75 6 Hypotenuse = 22.75 cm 7 Perimeter = 8.75+21+22.75 = 52.5 cm
What is the hypotenuse and perimeter of a right angle triangle when one side is 14 cm greater than the other side with an area of 240 square cm showing work?
1 Let the sides be x+14 and x 2 So: 0.5*(x+14)*x = 240 which transposes to x2+14x-480 3 Solving the above quadratic equation gives x a positive value of 16 4 Therefore the sides are 30 and 16 5 Using Pythagoras: 302+162 = 1156 and its square root is 34 6 Hypotenuse = 34 cm 7 Perimeter = 34+30+16 = 80 cm
What is the length of the hypotenuse of a right angle triangle when its area is 54 square cm and its perimeter is 36 cm showing how you achieved your answer?
according to the formulae : area of triangle = (1/2) x base of triangle x height 54=(1/2)xBxH B x H = 108 now we have to factorize it.. factors can be.. (12,9),(27,4)(18,6)(36,3) now its given perimeter=36 we have to check two condition for the tringle to be right angle triangle sum of two sides > third side sum of the square of the two sides of triangle(shorter sides)= square of the third side. only one factor (12,9) satisfies both the conditions.. so the third side comes out to be 36-(12+9)=15 so the sides are...12,9,15. that's your answer..
What are the side length of a right angle triangle with a hypotenuse of 17.42 cm and a perimeter of 40.20 cm showing work?
Let the sides be x and y:- x+y = 40.2-17.42 => y = 22.78-x Using Pythagoras: x^2+(22.78)^2 = 17.42^2 As a quadratic equation: 2x^2++215.472-45.56x = 0 Solving the equation: x = 6.7 cm and y = 16.08 cm Check: 6.7+16.08+17.42 = 40.20 cm which is its perimeter
What is the perimeter of a right angle triangle whose hypotenuse is 17 cm when one side is shorter than the other side by 7 cm showing work?
Let the sides be x and x-7 So using Pythagoras: x2+(x-7)2 = 172 => 2x2-14x-240 = 0 Solving the quadratic equation gives x a positive value of 15 Therefore sides are: 15 and 15-7 = 8 Perimeter: 17+15+8 = 40 cm
What is the perimeter of an isosceles triangle whose base is 15.96 cm with an area of 84.9072 square cm showing all work and answer?
These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.
Can you work out the length of the hypotenuse of a right angle triangle with sides VIII and VI inches showing all your workings in roman numerals?
Pythagoras' Theorem states that for any right angle triangle the height squared plus the base squared is equal to the square of the hypotenuse. In other words, after finding the square of the hypotenuse, square root your answer to find its length. Hence: (8*8)+(6*6)=64+36=100. The square root of 100=10. Therefore the length of the hypotenuse is 10 inches. In Roman numerals: (VIII*VIII)+(VI*VI)=LXIIII+XXXVI=C. The square root of C=X. Therefore the length of the hypotenuse is X inches. David Gambell, Merseyside, England.
What is the perimeter of a right angle triangle that has an hypotenuse of 20.8 cm and an area of 76.8 square cm showing work?
Square 20.8 and square (2*76.8) then find two numbers which have been squared that have a sum of 432.64 and a product of 23592.96 Let the squared numbers be x and y:- If: x+y = 432.64 Then: y = 432.64 -x If: xy = 23592.96 Then: x(432.64 -x) = 23592.96 So: 432.64x -x^2 -23592.96 = 0 Solving the above quadratic equation: x = 368.64 or x = 64 meaning y = 64 Square root of 368.64 = 19.2 and square root of 64 = 8 are sides of the triangle Therefore perimeter: 20.8+19.2+8 = 48 cm Check: 0.5*19.2*8 = 76.8 square cm Check: 19.2^2 + 8^2 = 432.64 and its square root is 20.8 which is the hypotenuse
What is the proof for showing that the sides of an isosceles right triangle are in the ratio of one to one to the square root of 2?
Augustus Pythagoras: let the equal sides be 1 unit. The square of the third side, which is the hypotenuse, is equal to the sum of the squares of the other two sides, in this case 12 and 12, a total of 2. The hypotenuse is therefore equal to the square root of two.
What is the hypotenuse and perimeter of a right angle triangle when one side is greater than the other side by 4.75 cm with an area of 135.375 square cm showing all work in logical stages?
1 Let the sides be: x+4.75 and x2 If: 0.5*(x+4.75)*x = 135.3753 Then: x2+4.75x-270.75 = 04 Using the quadratic equation formula: x has a positive value of 14.255 Therefore: sides are 14.25+4.75 = 19 cm and 14.25 cm6 Using Pythagoras: 192+14.252 = 564.0625 and its square root is 23.757 Hypotenuse: 23.75 cm8 Perimeter: 23.75+19+14.25 = 57 cm9 Check: 0.5*19*14.25 = 135.375 square cm
What is the hypotenuse and perimeter of a right angle triangle when one side is greater than the other side by 45.5 cm and having an area of 2535 square cm showing all work in step by step stages?
As an intermediate step, calculate the two sides adjacent to the right angle first. Once you have that, you can easily calculate the hypotenuse and the perimeter.You'll have to write an equation to calculate the sides. Use the equation for the area of a triangle. I suggest you set:"x" for one side"x + 45.5" for the other sideAnother Answer:-1 Let the sides be x+45.5 and x2 0.5*(x+45.5)*x = 2535 which transposes to: x2+45.5x-5070 = 03 Solving the above quadratic equation gives x a positive value of 524 So sides are 52+45.5 = 97.5 cm and 52 cm5 Using Pythagoras: 97.52+522 = 12,210.252 and its square root is 110.56 Hypotenuse = 110.5 cm7 Perimeter = 97.5+52+110.5 = 260 cm
