Suppose a square garden has an area represented by 9x^2 square feet. If one side is made 7 feet longer and the other side is made 2 feet shorter, then the trinomial that models the area of the larger garden is 9x^2 + 15x - 14 square feet.
Yes it is.
Explain
From the given area of the square, work out its sides in terms of x.
Find the area after these sides are lengthened and shortened by the given amount.
Hint: Since the area is 9x^2, the side length is 3x.
To find the trinomial that models the area of the larger garden, let's first write the expression for the area of the original square garden.
The original square garden has an area represented by 9x^2 square feet. Since it is a square, both sides of the garden have the same length. Let's denote the length of each side by 's'.
So, the area of the original square garden can be expressed as s^2 = 9x^2.
Now, according to the given information, one side of the garden is made 7 feet longer, and the other side is made 2 feet shorter. Therefore, the new length of one side is (s + 7), and the new length of the other side is (s - 2).
The area of the larger garden can be expressed as (s + 7)*(s - 2). Expanding this expression gives the trinomial that models the area of the larger garden.
So, let's expand (s + 7)*(s - 2):
(s + 7)*(s - 2) = s^2 - 2s + 7s - 14
= s^2 + 5s - 14
Now, substituting 9x^2 for s^2 in the above expression, we get:
9x^2 + 5s - 14
Therefore, the trinomial that models the area of the larger garden is 9x^2 + 5s - 14 square feet.