Find the unknown length.

Question

A right triangle has one leg that is twice as long as the other leg. The hypotenuse is 2sqrt(5) inches. Find the unknown lengths.

Answer 1

The Pythagorean theorem can be used to solve this problem.

The Pythagorean theorem states that for right triangles, a²+b²=c² where 'a' and 'b' are legs of the triangle and 'c' is the hypotenuse. We know the hypotenuse is 2√5 inches and we know one leg is twice as long as the other. Let's call the shorter leg 'x'. That would make the other leg, which is twice as long, '2x'.

Filling in our known values, we can use the Pythagorean theorem to solve for the unknown lengths:

(x)²+(2x)²=(2√5)²

x²+4x²=20

5x²=20

x²=4

x=±2

x must = 2 since a triangle can't have negative length legs.

If x is 2, then the missing legs of the triangles which are 'x' and '2x' are 2 inches and 4 inches.