Quadratic formula

Question

The hypothenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the length of the three sides of the triangle.

Answer 1

Need to use the Pythagorean theorem and we also need to define a variable for the length of the unknown leg.

Let x = length of the unknown leg.

So the hypotenuse, which is 3 times the length of the unknown leg, will be 3x.

Pythag Thm states a² + b² = c²

For us, a=x, b=4, and c=3x

Putting these into the Pythag Thm we get

(x)² + 4² = (3x)²

x² + 16 = 9x²

Subtract x² from both sides.

16 = 8x²

Divide both sides by 8

2 = x²

Take the square root of both sides.

x = √2