Question

The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is three feet. Find the lengths of the three sides of the triangle. Enter an exact answer. Do not type your answers as fractions or decimals.

Answer 1

a^2 + b^2 = c^2

Let c = hypotenuse = 2x

One of the legs = x. Let a or b = x.

I will let a = x. We can then say that b = 3.

3^2 + x^2 = (2x)^2

9 + x^2 = 4x^2

9 = 4x^2 - x^2

9 = 2x^2

9/2 = x^2

sqrt{9/2} = sqrt{x^2}

3/sqrt{2} = x

Rational denominator.

[3•sqrt{2}]/2 = x = a

Side 3 is given to be 3 feet. So, b = 3.

Hypotenuse = 2x

Hypotenuse = 2([3•sqrt{2}]/2)

Hypotenuse = 3•sqrt{2}

Understand?

The three sides are 3, [3•sqrt{2}]/2 and

3•sqrt{2}.