Pythagorean theorem

Question

The hypotenuse of a right triangle is 5 inches long. the shorter leg is 1 inch shorter than the longer leg. Find the lengths of the triangle.

Answer 1

Hi Laura,

 

The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle equals the square of the hypotenuse. 

 

The question says that the shorter leg is 1 inch shorter than the longer leg.  If we let X = the length of the longer leg, then X -1 is the length of the shorter leg.

 

Now let's plug into the formula --> X^2 + (X-1)^2 = 25

 

X^2 + X^2 - 2X + 1 = 25

 

2X^2 - 2X - 24 = 0

 

Divide everything by 2--> X^2 - X - 12 = 0

 

(X - 4) (X + 3) = 0

 

X = 4 . . . there can't be a negative length.

 

Then the shorter side is 3

 

Plug into the Pythagorean theorem to make sure that these numbers work.

 

Have fun.

 

Dan