The length of one leg of a right triangle is 8ft. The length of the hypotenuse is 2 feet longer that the other leg. Find the length of the hypotenuse leg.

Question

I'm having a lot of trouble trying to figure out this problem please could you help me 

Answer 1

Hi Becca, let x represent the length of the unknown leg. Then the hypotenuse will have a length of x + 2.

 

Using the Pythagorean Theorem:

 

A² + B² = C²

 

Substituting:

 

A = 8 feet

 

B = x feet

 

C = x + 2 feet

 

Solution:

 

8² + x² = (x + 2)²

 

64 + x² = x² + 4x + 4

 

The x² terms cancel out leaving and combining terms:

 

4x = 60

 

x = 15

 

The legs of the triangle:

 

Given leg: 8 feet

 

Other leg: x, or 15 feet

 

Hypotenuse: x + 2, or 17 feet

 

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