The hypotenuse of a right triangle is twice the length of one of its legs. The other leg is 15 feet. Find the length of the three sides

Answer 1

From the Pythagorean theorem we know that a² + b² = c^2.

We also know that one side is 15 feet and the hypotenuse is twice the length of the other side, So let's make a = 15 feet, then the hypotenuse becomes 2b (twice the length of the other side).

So now rewrite the equation by substituting for a and c, and a² + b² = c^2. becomes:

15² + b² = (2b)² , or 225 + b² = 4b²

subtract b² from both sides, giving 225 = 3b²

Next, divide by 3, and we have 75 = b,

Take the square root of both sides to get the length of side b, and b = 5√3.

The hypotenuse is twice the length of side b, so c = 10√3.

To check, plug the values back into the Pythagorean theorem:

15² + (5√3)² = (10√3)²

225 + 75 = 300, check.

Answer 2

draw and label a right triangle and use the Pythagorean Theorem; a^2+b^2=c^2 where a and b are the legs and c is the hypotenuse

a^2+b^2=c^2, where a=15, b=x, c=2x

15^2+x^2=(2x)^2

225+x^2=4x^2

4x^2-x^2=225

3x^2=225

x^2=75

take the square root of both sides

x=√75

x=√(25*3)=√25*√3=5√3

a=15, b=5√3, c=10√3

check: 15^2+(5√3)^2=(10√3)^2

225+75=300

300=300