The length of the longer leg is ? millmeters?

Question

One leg of a right triangle is 6 millimeters shorter than the longer leg and the hypotenuse is 6 millimeters longer than the longer leg.  What is the lengths of the sides of the triangle?

Answer 1

Let longer leg = x

Let other leg = x - 6

Let hypotenuse = x + 6

 

Using the Pythagorean theorem,

 

x² + (x - 6)² = (x + 6)²

x² + x² - 12x + 36 = x² + 12x + 36

2x² - 12x + 36 = x² + 12x + 36

2x² - 12x = x² + 12x

 

x² - 24x = 0         ------> quadratic equation

 

x(x - 24) = 0

 

Set the factors equal to zero and solve for x.  Choose the positive value of x.  Then, plug it into the variables to find the other leg and hypotenuse.

Answer 2

Let the longer leg = x

The shorter leg = x - 6

The hypotenuse = x + 6

 

Using the Pythagorean Theorem, we have:

 

x² + (x - 6)² = (x + 6)²

x² + x² - 12x + 36 = x² + 12x + 36

2x² - 12x + 36 = x² + 12x + 36

x² - 24x = 0

x(x - 24) = 0

x = 0 and x = 24

 

Since the leg of a triangle cannot equal 0, then x = 24 is the only valid solution.

 

The triangle has side lengths of 24 mm, 24 + 6 = 30 mm, and 24 - 6 = 18 mm