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What are the dimensions of a right angle triangle when its perimeter is 4 times its base with an area of 13.5 square cm showing all aspects of work?
The answer is 4.5 cm, 6.0 cm and 7.5 cm.
This browser has stopped supporting superscripts so I will use sq for squared numbers and sqrt for square roots.
Suppose the three sides are x y and z cm, that the base is x and the other leg is y so that the hypotenuse is z.
Perimeter = 4*x => x+y+z = 4x and therefore y+z = 3x .. .. .. .. (1)
Next, Area = 13.5 sq cm => 0.5*x*y = 13.5,
=> x*y = 27 or y = 27/x and so, substituting for y in (1) gives 27/x + z = 3x
and therefore, z = 3x - 27/x
so that sq(z) = 9*sq(x) - 162 + sq(27/x) .. .. .. .. .. .. .. .. .. .. (2)
Finally, by Pythagoras sq(x) + sq(y) = sq(z)
=> sq(x) + sq(27/x) = sq(z) .. .. .. .. .. .. .. .. .. .. .. .. (3)
Equating (2) and (3)
9*sq(x) - 162 + sq(27/x) = sq(x) + sq(27/x)
=> 8*sq(x) = 162 => sq(x) = 162/8 = 20.25
=> x = sqrt(20.25) = 4.5
Then y = 27/x = 27/4.5 = 6.0
and z = 3x - 27/x = 13.5 - 6 = 7.5
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What are the dimensions of a rectangle that has a perimeter of 19.8 cm and an area of 24.3 square cm showing work?
Divide the perimeter by 2 then find two numbers that have a sum of 9.9 and a product of 24.3 which will work out as 5.4 and 4.5 by using the quadratic equation formula. Check: 2*(5.4+4.5) = 19.8 cm which is the perimeter Check: 5.4*4.5 = 24.3 square cm which is the area Therefore the dimensions of the rectangle are: 5.4 cm and 4.5 cm
What is the largest angle of a triangle with sides of 5.8cm by 14.1cm by 8.3cm showing work?
Such a triangle would be impossible to construct with the given 3 dimensions because in order to construct a triangle the sum of its 2 shortest sides must be greater than the length of its longest side.
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.
What is the perimeter of an isosceles triangle whose base is 15.96 cm with an area of 84.9072 square cm showing all aspects of work with answer?
First find its height by dividing its area and use Pythagoras to find its sides: Height: 84.9072/(0.5*15.96) = 10.64 cm Half its base: 7.98 cm Pythagoras: 10.64 squared plus 7.98 squared = 176.89 and its sq rt = 13.3 Perimeter therefore is: 2*(13.3)+15.96 = 42.56 cm
What are the dimensions of a rectangle when one side is 3 cm longer than the other side and its area is twice its perimeter in square cm showing work with answers?
Let the dimensions be x and x+3 Perimeter: 4x+6 Area: x(x+3) = 2(4x+6) => x^2 +3x = 8x+12 => x^2 -5x-12 = 0 Solving the above quadratic equation: x has a positive value of 6.77 rounded to 2dp Therefore dimensions are: 6.77 cm and 9.77 cm
What are the dimensions of a rectangle that has a perimeter of 19.8 cm and an area of 24.3 square cm showing work?
Divide the perimeter by 2 then find two numbers that have a sum of 9.9 and a product of 24.3 which will work out as 5.4 and 4.5 by using the quadratic equation formula. Check: 2*(5.4+4.5) = 19.8 cm which is the perimeter Check: 5.4*4.5 = 24.3 square cm which is the area Therefore the dimensions of the rectangle are: 5.4 cm and 4.5 cm
What is the largest angle of a triangle with sides of 5.8cm by 14.1cm by 8.3cm showing work?
Such a triangle would be impossible to construct with the given 3 dimensions because in order to construct a triangle the sum of its 2 shortest sides must be greater than the length of its longest side.
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.
What is the perimeter of an isosceles triangle whose base is 15.96 cm with an area of 84.9072 square cm showing all aspects of work with answer?
First find its height by dividing its area and use Pythagoras to find its sides: Height: 84.9072/(0.5*15.96) = 10.64 cm Half its base: 7.98 cm Pythagoras: 10.64 squared plus 7.98 squared = 176.89 and its sq rt = 13.3 Perimeter therefore is: 2*(13.3)+15.96 = 42.56 cm
What are the dimensions of a rectangle when one side is 3 cm longer than the other side and its area is twice its perimeter in square cm showing work with answers?
Let the dimensions be x and x+3 Perimeter: 4x+6 Area: x(x+3) = 2(4x+6) => x^2 +3x = 8x+12 => x^2 -5x-12 = 0 Solving the above quadratic equation: x has a positive value of 6.77 rounded to 2dp Therefore dimensions are: 6.77 cm and 9.77 cm
What is the perimeter of an equilateral triangle whose area is 97.428 square cm showing work and answer to the nearest integer?
Let the sides be s:- If: 0.5*s squared*sin(60 degrees) = 97.428 Then: s = square root of 97.428*2/sin(60 degrees) => 15.00001094 Perimeter: 3*15 = 45 cm
What are the dimensions of a rectangle that has an area of 600 square cm and a perimeter of 1 m showing work?
I suggest that you do the following:* Convert the meters to centimeters, to have compatible units.* Write the equation for the area of the rectangle. Replace the variable "a" (area) with the known area.* Write the equation for the perimeter of a rectangle. Replace the variable for the perimeter with the known perimeter (in cm).* Use any method to solve the simultaneous equations.Another Answer:-Let the dimensions be x and yIf: 2x+2y = 100 then x+y = 50 and x = 50-yIf: xy = 600 then (50-y)y = 600 and so 50y-y2-600 = 0Solving the quadratic equation: y = 20 or y = 30Therefore by substitution the dimensions are: when y = 20 cm then x = 30 cm
What are the dimensions of a regular triangle whose area in square cm is 16 times the square root of 3 showing work?
It must be an equilateral triangle if it's a regular shape and so:- If: 0.5*side2*sin(60) = 16*square root of 3 Then: its sides are 8 cm by making 'side' the subject of the above equation
Why when the US flag is folded what shape is it?
it should be a triangle with no red showing
What is the perimeter of a rectangle whose diagonal is 17.55 cm with an area of 109.35 square cm showing key aspects of work?
Here are the key aspects of work; I'll leave the details of the calculation to you. 1) Write an equation for the area, in terms of variables "w" and "h" (for width and height). 2) Write an equation for the length of the diagonal, in terms of "w" and "h". (Hint: Use the Pythagorean Theorem.) 3) Solve the two equations. 4) Calculate the perimeter, based on length and width.
What is the area of a rhombus when one of its diagonals is 11.8 cm in length and has a perimeter of 29 cm showing work and answer?
Perimeter = 29 cm so each side is 7.25 cm. The triangle formed by the diagonal and two sides has sides of 7.25, 7.25 and 11.8 cm so, using Heron's formula, its area is 24.9 square cm. Therefore, the area of the rhombus is twice that = 49.7 square cm.
What are the dimensions of an isosceles triangle when each of its congruent sides is a number squared with as base of 3 times the same number and has a perimeter of 77.2502 cm showing work and answer?
Let the number be x and so: 2x squared+3x = 77.2502 Then: 2x squared+3x-77.2502 = 0 Solving the above quadratic equation gives x a positive value of 5.51 Thus: congruent sides are each 30.3601 cm and base is 16.53 cm Check: 30,3601+30.3601+16.53 = 77.2502 cm
