An isosceles right triangle has legs measuring (x – 2) cm each. The hypotenuse has measure (x + 4) cm. Find x.

Question

An isosceles right triangle has legs measuring (x – 2) cm each. The hypotenuse has measure (x + 4) cm. Find x.

Answer 1

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

 

x² - 4x + 4 + x² - 4x + 4 = x² + 8x + 16

 

x² - 16x - 8 = 0

 

x =   16 ± √[(-16)² - 4(1)(-8)]

                  2(1)

 

  =   16 ± √288

           2

 

  =   16 ± 12√2

           2

 

   = 8 ± 6√2 ≈ 16.48, -0.48

 

Since a negative value for x makes no sense in this context, 

   x = 8 + 6√2