Answer:
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
