Mark, this is the solution:
Let x to represent the length of the shorter leg of the right triangle. Thus,
x + 4 = Longer leg
x + 8 = Hypotenuse
Now, we use the Pythagorean theorem to solve for x, this way:
(x + 8)² = (x + 4)² + x²
x² + 16x + 64 = x² + 8x + 16 + x²
Like terms:
-x² +8x + 48 = 0
Multiplying by -1 at both sides:
x² - 8x - 48 = 0
(x -12) (x + 4) = 0
x1 = 12
x2 = -4
We take x1 because the length of a side can't be a negative value. In consequence, we have:
• Shorter leg = 12 cm
,
• Longer leg = 16 cm
,
• Hypotenuse = 20 cm
