The hypotenuse of a right triangle is 24 feet long. The length of one leg is 22 feet more than the other. Find the lenghts of the legs

Question

The hypotenuse of a right triangle is 24 feet long. The length of one leg is 22 feet more than the other. Find the lenghts of the legs

Answer 1

Hi Ricky, use the Pythagorean Theorem, a² + b² = c². Let x be the length of one leg, then x + 22 is the length of the other leg. The hypotenuse is 24 feet.

 

Substitute in to the formula:

 

x² + (x + 22)² = 24²

 

Solve for x:

 

x² + x² + 44x + 484 = 576

 

Subtract 576 from both sides and combine terms:

 

2x² + 44x - 92 = 0

 

Divide all terms by 2:

 

x² + 22x - 46 = 0

 

Use the quadratic formula to find x:

 

x = (-22 ± √(22² - ( 4 * 1 * -46))) / (2 * 1)

 

x = (-22 ± 25.846) / 2

 

x = (-22 - 25.846) / 2 

 

x = -47.846 / 2

 

x = -23.923, this solution can be discarded because the length of the leg cannot be negative.

 

x = (-22 + 25.846) / 2

 

x = 3.846 / 2

 

x = 1.923

 

One leg of the triangle is 1.923 feet in length.

 

The other leg is x + 22 feet, or 23.923 feet in length.

 

Check:

 

1.923² + 23.923² = 24²

 

3.70 + 572.30 = 576

 

576 = 576, values check.

 

Questions?

 

 

Answer 2

Let the length of the shortest side be x on let's apply pythagoras' theorem

 

c^2 = a^2 + b^2

 

24^2 = x^2 + (x + 22)^2

 

576 = x^2 + x^2 + 44x + 484

 

2x^2 + 44x - 92 = 0

 

x^2 + 22x - 46 = 0

 

x= 1.923

 

so our legs would be 

 

1.923, 23.923 and 24