The hypotenus of a right triangle is 6 feet long. One leg is 2 feet shorter than the other. Find the lengths of the legs. Round to the nearest tenth of a foot.

Question

The hypotenus of a right triangle is 6 feet long. One leg is 2 feet shorter than the other. Find the lengths of the legs. Round to the nearest tenth of a foot.

Answer 1

Hi Kara, let x represent the length of one let of the right triangle. Then the other leg is: x - 2.

 

Use the Pythagorean Theorem to solve:

 

a² + b² = c²

 

Let a = x

 

Let b = x - 2

 

Let c = 6

 

Substitution

 

x² + (x - 2)² = 6²

 

x² + x² - 4x + 4 = 36

 

Combine like terms:

 

2x² - 4x - 32 = 0

 

Divide entire equation by 2:

 

x² - 2x - 16 = 0

 

 

Use the quadratic formula to solve:

 

x = 5.12 and -3.12. We can discard the -3.12 result since the leg cannot be negative.

 

One leg is 5.1 feet long.

 

The other leg is: 5.1 - 2, or 3.1 feet long.

 

Questions?

Answer 2

One leg = x

Other leg = x + 2

Hypotenuse = 6

 

Use the Pythagorean theorem.

 

x² + (x + 2)² = 6²

 

x² + x² + 4x + 4 = 36

 

2x² + 4x - 32 = 0

 

 

Solve the quadratic equation for x.  Then accept the positive value of x.  Once you have your value of x, use it to find the other side.