SOLUTION: A flower garden is in the shape of a right triangle. The longest side of the triangle measures 13 m. One of the shorter sides is 7 m longer than the other. Determine the length of

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A flower garden is in the shape of a right triangle. The longest side of the triangle measures 13 m. One of the shorter sides is 7 m longer than the other. Determine the length of       Log On


   

Question 952766: A flower garden is in the shape of a right triangle. The longest side of the triangle measures 13 m. One of the shorter sides is 7 m longer than the other. Determine the length of the shortest side.
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
Since the triangle is right triangle you can use the Pythagorean theorem to find the lengths of each side a%5E2%2Bb%5E2=c%5E2 where c is the hypotenuse and a and b are the lengths of the sides.

The longest side of every right triangle is the hypotenuse so right away we know that c=13.

To calculate the sides you need to make separate equations. One side is a=x and the other is b=7%2Ba. This is because it says "One of the shorter sides is 7 m longer than the other" which can be translated into the equation 7%2Bx which leaves the remaining side as simply x.

Plug these equations into the Pythagorean Theorem.
c=13
a=x
b=7%2Bx

a%5E2%2Bb%5E2=c%5E2
x%5E2%2B%287%2Bx%29%5E2=13%5E2
Distribute then solve for x to find the shortest side.
x%5E2%2Bx%5E2%2B14x%2B49=169
2x%5E2%2B14x-120=0
x%5E2%2B7x-60=0
x%2B12%29%28x-5%29=0
x=-12 x=5
The value is 5 because a length cannot be negative.