A rectangular garden has length of x+2 and width of 2x-3, and the area of the garden is 72 square feet. What are the dimensions of the garden?

Answer 1

(x+2)* (2x-3) = 72

This is a quadratic equation; solve for x.

Answer 2

Hello, thank you for taking the time to post your question!

The general formula that you want to use here is that

Area = Length x Width, so plugging in the values that are given that becomes

72 = (x + 2)(2x – 3)

72 = 2x^2 + 4x – 3x – 6

72 =  2x^2 + x – 6

0 = 2x^2 + x – 78

At this point you can use the quadratic formula to solve for the values of x. The one that meets are criteria here is x = 6 because the dimensions have to be positive. Going back to the original length and width functions to find the exact values gives

Length = 6 + 2 = 8

Width = 2(6) – 3 = 9

So the dimensions of the garden are 8 ft by 9 ft

I hope that helps get you moving in the right direction! Feel free to reach out if you still have questions beyond that :)

Answer 3

Here is a quick visual example of how to go about solving this problem by hand.

Answer 4

(x+2)(2x-3) = 72

2x² + x - 6 = 72

2x² + x - 78 = 0

(2x +13)(x - 6) = 0

x = -13/2 or x = 6

If x = -13/2, then 2x - 3 < 0. Since the width can't be negative, -13/2 is not a viable solution.

So, x = 6.

Length = x + 2 = 8 ft and Width = 2x - 3 = 9 ft

Answer 5

(x + 2)(2x - 2) = 72

Solve for x using Algebra 1 methods.