The longer leg of a right triangle is 4 cm longer than the shorter leg. The hypotenuse is 8 cm longer than the shorter leg. Find the side lengths of the triangle.

Answer 1

The sides are 12, 16, and 20

For a Right Triangle we can use the Pythagorean Theorem

Let x = Short Leg

x + 4 = Longer Leg

x + 8 = Hypotenuse

x² + (x + 4)² = (x + 8)²

x² + x² + 8x + 16 = x² + 16x + 64

Combine like terms

2x² + 8x + 16 = x² + 16x + 64

Subtract x², 16x and 16 from both sides of the equation to give

2x² - x² + 8x - 16x = 64 - 16

x² - 8x = 48

We can set up a quadratic to find x

x² - 8x - 48 = 0

(x - 12)(x + 4)

x cannot be negative so x = 12

x = 12 = Shortest Side

x + 4 = 16 = Longer Side

x + 8 = 20 = Hypotenuse

Checking

12² + 16² = 20²

144 + 256 = 400

400 = 400

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