Question

The hypotenuse of a right triangle is twice the length of one of its legs. The length of the other leg is 9 feet. Find the length of the three sides of the triangle. Answer exactly or round to 2 decimal places.

Answer 1

Answer:

3 sides = 5.20 feet, 9 feet, and 10.40 feet

Step-by-step explanation:

Let's understand the pythagorean theorem first.

It says that in any right triangle, the lengths of 3 sides are related by:

Hypotenuse ^ 2 = One Leg ^2 + Another Leg ^ 2

Hypotenuse is TWICE of one leg. Let one leg be "x", so hypotenuse would be "2x"

And, another leg is given as 9. Now we can use pythagorean theorem and write:

$(2x)^2=x^2+9^2$

We solve this equation for x and find the 3 lengths respectively. Shown below:

$(2x)^2=x^2+9^2\\4x^2=x^2+81\\4x^2-x^2=81\\3x^2=81\\x^2=\frac{81}{3}\\x^2=27\\x=5.20$

Hypotenuse = 2x = 2(5.20) = 10.40

THus, we can say

3 sides of the triangle measure 5.20 feet, 9 feet, and 10.40 feet