Solve for centimeters of a right triangle!

Question

The larger leg of a right triangle is 3 cm longer than its smaller leg. The hypotenuse is 6 cm longer than the smaller leg. So how many centimeters long is the smaller leg? 

Answer 1

Hi Angle, let x represent the shorter leg. Then the length of the longer leg will be x + 3 and the length of the hypotenuse will be x + 6.

 

Using the Pythagorean Theorem, you get:

 

x² + (x + 3)² = (x + 6)²

 

This becomes:

 

x² + x² + 6x + 9 = x² + 12x + 36

 

Combine terms:

 

x² - 6x - 27 = 0

 

Factor:

 

(x - 9) * (x + 3) = 0

 

Using the zero product rule:

 

x - 9 = 0

 

x = 9

 

And

 

x + 3 = 0

 

x = -3, this solution can be discarded since the leg of a triangle cannot be negative.

 

Solution:

 

The length of the shorter leg is 9 centimeters.

 

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