PLS READ CAREFULLY BC THERE IS A SIMILAR PROBLEM
A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to twice the number of units in the sum of the lengths of its legs. What is the sum of all the different possible areas of cool right triangles?
Answer is not 396, Pls answer HERE
2(x + y) = 1/2*x*y
4x + 4y - xy = 0
4x + y(4 - x) = 0
y = 4x/(x - 4)
Therefore, x > 4, y > 4 since x and y must both be positive.
the only positive integer x values that give positive integer y values are 5,6,8,12,and 20
But i just realized that is not what you asked.
(5,20) area = 0.5*5*20 = 50
(6,12) area = 0.5*6*12 = 36
(8,8) area = 0.5*8*8 = 32
(12,6) area is 36
(20,5) area is 50
so sum of all possible areas is 50+36+32 = 118 units squared.
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Thanks for answering guest.
I assume that when you say "legs" you mean the 3 sides of the triangle. If that is so, then:
I can find only 1 such right triangle:
9^2 + 40^2 = 41^2
Area = (9 x 40) / 2 = 180 u^2
Sum of its 3 sides = 9 + 40 + 41 = 90 u
So, the area is 2 times the sum of the 3 sides of the triangle.