Justine wants to put a deck in the corner of her backyard in the shape of a right triangle. The length of one side of the deck is 7 feet more than the other side. The hypotenuse is 13. Find the lengths of the two sides of the deck.

5

12

Step-by-step explanation:

Let x = length of a side of the deck

Let x - 7 = length of the other side.

Now let's use the Pythagorean Theorem.

a² + b² = c²

a = x

b = x+7

c = 13

Now that we have our values, let's plug them in.

x² + (x+7) ² = 13²

x² + x² + 14x + 49 = 169

2x² + 14x + 49 = 169

Since it's a quadratic equation, we get 0 on one side.

2x² + 14x - 120 = 0

Now we factor out the greatest common factor

2 (x²+7x-60) = 0

2 (x + 12) (x - 5) = 0

Using the Zero product property, we get:

2 ≠ 0

x + 12 = 0

x = - 12

x - 5 = 0

x = 5

Since x is a side of the triangle, x = - 12 does not get included. So then we have:

x = 5

Now let's solve for the other side.

x + 7

5 + 7 = 12

Now that we have our value of x, let's put it in the formula to check.

x = 5

a² + b² = c²

x² + (x+7) ² = 13²

5² + (5+7) ² = 13²

25 + 144 = 169

169 = 169