The hypotenuse of a right triangle is 1 cm longer than the longer leg. The shorter leg is 17 cm shorter than the longer leg. fFind the length of the longer leg

Question

The hypotenuse of a right triangle is 1 cm longer than the longer leg. The shorter leg is 17 cm shorter than the longer leg. Find the length of the longer leg of the triangle.

 

I have to answer the question in  cm, cm^2, or cm^3

 

 

 

 

Answer 1

Let L represent the length of the longer leg. The hypotenuse is L + 1 and the shorter leg's length is L - 17. By the Pythagorean theorem,

 

(L - 17)^2 + L^2 = (L + 1)^2

 

Thus

 

(L^2 - 34L + 289) + L^2 = L^2 + 2L + 1

 

L^2 -36L + 288 = 0

 

(L - 12)(L - 24) = 0

 

L = 12 cm or 24 cm

 

Since 12 cm is less than 17 cm, the solution L = 12 cm is extraneous. Therefore, L = 24 cm. [Note that the triangle has Pythagorean triple 7,24,25.]