The hypotenuse of a right triange is 50 ft. One leg is 10 ft longer than the other. What are the lenghts of the leg?

Question

This is a question on my math review. It is a calculator problem and I am not sure how to start it. 

Answer 1

A right triangle indicates we can use the Pythagorean theorem.

 

 

The sum of the squares of the two legs equals the square of the hypotenuse.

 

Let one leg = x

Let the other leg = x + 10

Let the hypotenuse = 50

 

 

Set up the equation using the variables and formula for Pythagorean theorem.

 

x² + (x + 10)² = 50²

 

x² + (x² + 20x + 100) = 2500

 

2x² + 20x + 100 = 2500

 

 

Subtract 2500 on both sides of equation.

 

2x² + 20x - 2400 = 0

 

 

Factor out a 2.

 

2(x² + 10x - 1200) = 0

 

 

Set the term in parenthesis equal to zero.

 

x² + 10x - 1200 = 0

 

 

Use the quadratic formula to solve for x.

 

x = (-b ± √(b² - 4ac)) / 2a

 

where:

a = 1

b = 10

c = -1200

 

 

Plug in these values into the formula.  You will get two solutions.  Accept the positive value of x and substitute it into the variables to get your leg lengths.