Question

The legs of a right triangle have lengths x+2 and x+6. The hypotenuse has length 2x. Find the perimeter of the triangle

Answer 1

Answer:

The perimeter is 12 + 16 + 20 = 40

Step-by-step explanation:

By Pythagoras' Theorem:

(x+2)² + (x+6)² = (2x)²

=> x² + 4x + 4 + x² + 12x + 36 = 4x²

=> 2x² - 16x - 40 = 0

=> x² - 8x - 20 = 0

=> ( x - 10 ) ( x + 2 ) = 0

=> x = 10 or x = -2

=> x = 10, since the hypotenuse has length 2x and this must be positive.

So the legs have lengths 12 and 16, and the hypotenuse has length 20.

The perimeter is 12 + 16 + 20 = 40.