Question

the longer leg of a right triangle is 4 cm longer than the shorter leg. the hypotenuse is 8cm longer than the shorter leg. Find the side length of the triangle.length of the shorter leg__cm length of the longer leg__cmlength of the hypotenuse ___cm

Answer 1

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