Question

Suppose a right triangle has one leg of the length 5cm. The hypotenuse is twice as long as the other leg. Find the missing two sides of the right triangle

Answer 1

According to the Pythagorean Theorem, x^2 + y^2 = hyp^2.

Let x = 5cm be one leg.

If the hyp is twice as long as the other leg, then hyp = 2y.

Then x^2 + y^2 = hyp^2 becomes

(5 cm)^2 + y^2 = (2y)^2. We need to solve this for y.

25 cm^2
25 cm^2 + y^2 = 4y^2, or 25 cm^2 = 3y^2. Then y^2 = --------------
3

and y = + sqrt( [25 cm^2] / 3 ), or y = + 5 / sqrt(3), or y = 5sqrt(3) / 3.

The "other side" thus has length y = 5sqrt(3) / 3

and the hyp has length 2y = 2 [ 5sqrt(3) / 3 ] = 10 sqrt(3) / 3