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What is the perimeter and area of a right angle triangle whose hypotenuse is 17.5 cm and with one side being greater than the other side by 3.5 cm showing key stages of work?
Wiki User
∙ 10y ago
1 Let the sides be: x+3.5 and x
2 Using Pythagoras: (x+3.5)(x+3.5)+x2 = 17.52
3 So it follows: 2x2+7x-294 = 0
4 Solving the quadratic equation: x has a positive value of 10.5
5 Perimeter: (10.5+3.5)+10.5+17.5 = 42 cm
6 Area: 0.5*14*10.5 = 73.5 square cm
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∙ 10y ago
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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 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 equation of a circle that passes through the points of 5 5 and 8 5 and 5 1 on the Cartesian plane showing work?
The points will form a right angle triangle in a circle whose hypotenuse is its diameterLength from (8, 5) to (5, 1) = 5Midpoint: (6.5, 3) which is the centre of the circleRadius: 2.5Equation of the circle: (x-6.5)^2+(y-3)^2 = 6.25
What is the area and perimeter of a rhombus whose diagonals are in lengths of 7.5 cm and 10 cm showing work?
Area of the rhombus: 0.5*7.5*10 = 37.5 square cm Perimeter using Pythagoras: 4*square root of (3.75^2 plus 5^2) = 25 cm
Argument to showing that an equilateral triangle cannot have a right angle?
If you have an equilateral triangle ABC, then draw the line from A to D, the mid point of BC. Then in trangles ABD and ACD, AB = AC (equilateral), BD = DC (D is midpoint), and AD is common so these two triangles are congruent and so angle ABD = angle ACD. That is, angle ABC = angle ACB. Similarly the third angle can be shown to be the same. Thus an equilateral triangle is also equiangular. Now, sum of the interior angles of any triangle is 180 degrees. So since sum of three equal angles measures is 180 degrees, they must be 60 degrees each, i.e. NOT 90 degrees so there is no right angle..
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 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 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 perimeter of a right angle triangle whose height is greater than its base by 1.45 cm and has an area of 12.615 square cm showing work in progressive stages?
1 Let its height be x+1.45 and its base be x2 So: 0.5*(x+1.45)*x = 12.615 multiply both side by 23 Therefore: x2+1.45x-25.23 = )4 Using quadratic equation formula gives x a positive value of 4.355 It follows: height = 5.8 and base = 4.356 Using Pythagoras: hypotenuse = 7.257 Perimeter: 5.8+4.35+7.25 =17.4 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
What is the hypotenuse and perimeter of a right angle triangle when one of its sides is greater than the other side by 262.5 mm which has an area of 421.875 square cm showing all aspects of work?
1 Let the sides be (x+26.25 cm) and x cm2 If: 0.5*(x+26.25)*x = 421.875 => x2+26.25x = 421.875*23 Then: x2+26.25x-843.75 = 04 Solving the above quadratic equation gives x a positive value of 18.755 Therefore sides are:18.75+26.25 = 45 cm and 18.75 cm6 Using Pythagoras: 452+18.752 = 2376.5625 and its square root is 48.757 Hypotenuse: 48.75 cm8 Perimeter: 48.75+45+18.75 = 112.5 cm9 Check: 0.5*45*18.75 = 421.875 square cm
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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 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.
