The shorter leg of a right triangle is 7 cm shorter than the longer leg. The hypotenuse is 7 cm longer than the longer leg. Find the side lengths of the triangle.

Answer 1

Let' s use the variable x to represent the length of the longer leg.

Then we can represent the length of the hypotenuse with the following expression: x + 7

Also the length of the shorter leg can be represented by: x - 7

Using the Pythagorean Theorem , a² + b² = c², we can write:

(x - 7) ² + x² = (x + 7)²

Solving this equation:

x² - 14x + 49 + x² = x² + 14x + 49

2•x² - 14 x + 49 = x² + 14 x + 49

2•x² - 14 x + 49 - x²= x² + 14 x + 49 - x²

x² -14 x + 49 = 14 x + 49

x² -14 x + 49 - 49 = 14 x + 49 - 49

x² -14 x = 14 x

x² -14 x + 14 x = 14 x + 14 x

x² = 28 x

x² /x = 28x/x

x = 28

The longer leg would be 28 cm

The hypotenuse would be x + 7 = 28 + 7 = 35 cm

The shorter leg would be x -7 = 28 - 7 = 21 cm