Question

find the lengths of the legs of a right triangle if it is known that sum of the lengths is 23cm, and the area of the triangle is 60cm^2

Answer 1

15 and 8

Explanation:

Let the legs be a, b

a+b=23

ab=120

Then, 23b-b^2=120. so b^2-23b+120=0. Thus (b-8)(b-15)=0. Thus b=8,15, and if b=8, then the other length a is 15.