SOLUTION: Problem: ABC is a right triangle. The length of its perimeter is equal to 60 units and the size of its area is equal to 150 units squared. Find the two sides and hypotenuse.

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Question 500319: Problem:
ABC is a right triangle. The length of its perimeter is equal to 60 units and the size of its area is equal to 150 units squared. Find the two sides and hypotenuse.
Answer by cleomenius(959) (Show Source):
You can put this solution on YOUR website!
Area f triangle = 150 = 1/2ab
ab = 300
a^2 + b^2 = c^2.
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a + b + c = 60; the perimeter.
a+ b = 60 - c rearrangement.
square both sides.
(a + b)^2 = (60 - c)^2
a^2 + 2ab + b^2 = 3600 + c^2 - 120c
subtract the equation A^2 + b^2 = c^2 (simultaneous equations)
2ab = 3600 - 120c
ab is known to be 300, hence
600 = 3600 - 120c
-3000 = -120c
25 = c
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substitute c by 25 in the equation a + b + c = 60 to obtain
a + b + 25 = 60
a + b = 35
Since AB = 300 then b = 300/a which is substituted into the equation a + b = 35
a + 300/a - 35 = 0
multiply all terms by a.
a^2 -35a + 300 = 0
Solve our quadratic equation.
(x -15)(x - 20)
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15, 20, 25 are our dimensions.
15 + 20 + 25 = 60 units perimeter.
This does check.
15 * 20 = 300 units area.
This does check.
15^2 + 20^2 = 25^2
225 + 400 = 625 units.
This does check also.
Cleomenius