Find the lengths of each side of the following right triangles.

Question

In triangle F, the shorter leg is 1 less than one-third of the longer leg while the hypotenuse is 1 more than the longer leg.

 

 

 

 

 

 

 

Short leg=            Long leg=            Hypotenuse=             

 

 

 

Answer 1

Based on the information in the problem, the lengths of the three sides are:

 

Longer leg = x

Shorter leg = x/3 - 1

Hypotenuse = x + 1

 

So, according to the Pythagorean theorem:

 

x^2 + (x/3 - 1)^2 = (x + 1)^2

 

x^2 + (x^2)/9 - 2x/3 + 1 = x^2 + 2x + 1

 

(x^2)/9 - 8x/3 = 0

Factors are (x/3) and (x/3 - 8)

 

x/3 = 0, so x = 0

 

This won't work because the shorter side will have a negative length.

 

x/3 - 8 = 0

 

x/3 = 8

 

x = 24

 

Sides are 24, 7, and 25.

 

Check:  576 + 49 = 625