Right triangle solve for x

Question

Find the length of each side of a right triangle with sides x and 3x +3, and a hypotenuse of 4x-3.

Answer 1

By Pythagoras

 

x² + (3x + 3)² = (4x - 3)²

 

Can you solve for x and answer?

Answer 2

By the Pythagorean Theorem, x² + (3x+3)² = (4x-3)²

 

   x² + 9x² + 18x + 9 = 16x² - 24x + 9

 

         6x² - 42x = 0

 

         6x(x - 7) = 0       x = 0 or x = 7

 

Since x can't be 0, x = 7

 

So, x = 7     3x+3 = 24    and 4x-3 = 25

 

Answer 3

x² + 9x²+ 18x + 9 = 16x² - 24x + 9

6x² - 42x = 0

6x(x - 7) = 0

 

6x = 0

x = 0

 

x - 7 = 0

x = 7

 

Let's check.

 

0² + (3(0) + 3)² = (4(0) - 3)²

0 + 3² = (-3)²

9 = 9

0 = 0

Check.

 

7² + (3(7) + 3)² = (4(7) - 3)²

49 + (21 + 3)² = (28 - 3)²

49 + 576 = 625

625 = 625

0 = 0

Check.

 

x = 0 or x = 7