The answer is 17, 5.
We are given two things :
- Length exceeds width by 12 inches
- Area = 85 square inches
We can represent the length and width as x + 12 and x respectively.
Now, the formula for the area of a rectangle is :
Area = Length x width
Now, let's substitute the values for length and width in the formula along with the area.
- (x + 12)(x) = 85
- x² + 12x = 85
- x² + 12x - 85 = 0
We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.
- x² + 17x - 5x - 85 = 0
- x (x + 17) - 5 (x + 17) = 0
- (x + 17)(x - 5) = 0
- x = 17, 5