Thread: Finding the sides of a triangle given altitude and hypotenuse

The perimeter of a right triangle is 60 and the altitude
on the hypotenuse is 12. Find the sides of the triangle.

Originally Posted by Statsnoob2718

The perimeter of a right triangle is 60 and the altitude
on the hypotenuse is 12. Find the sides of the triangle.

look to the picture

the perimeter 60

a+b+c = 60

and since we have a right triangle

a^2 = b^2 + c^2

we have another equation the area

1/2 * base *altitude find it consider a as base , and another time consider b base so

$\displaystyle \frac{1}{2} a (12) = \frac{1}{2} b c $

three equations solve them