Answer:
the length of the rectangle is y - 3.
Explanation:
To find the length of the rectangle, we need to use the formula for the area of a rectangle:
Area = length x width
We are given the area of the rectangle as y^2 + 2y - 15 and the width as y + 5.
Let's substitute these values into the formula:
y^2 + 2y - 15 = length x (y + 5)
Now, we can solve for the length by dividing both sides by y + 5:
length = (y^2 + 2y - 15) / (y + 5)
We can simplify this expression by factoring the numerator:
length = [(y + 5)(y - 3)] / (y + 5)
The (y + 5) term in the numerator and denominator cancel out, leaving us with:
length = y - 3
Therefore, the length of the rectangle is y - 3.