Question

A brace for a shelf has the shape of a right triangle. its hypotenuse is 14 inches long and the two legs are equal in length. how long are the legs of the? triangle?

Answer 1

To answer this item, we make use of the equation derive from the Pythagorean theorem for right triangles which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. If we let x be the measure of both the shorter sides (we call this as legs), we have,
                         (14 in)² = (x²) + (x²)
Simplifying the equation,
                         196 in² = 2x²
Divide both sides of the equation by 2,
                         98 in² = x²
To get the value of x, we get the square root of both sides of the equation,
                         x = sqrt (98) = 7√2 inches

Hence, the measure of each leg of the right triangle is 7√2 inches or approximately 9.9 inches.