the length of a rectangle flower garden

Question

the length of a rectangle flower garden is 2 feet less than triple the width. The area of the flower garden is 176 square feet. Find the length and the width of the flower garden.

Answer 1

Hi Ezra,

Let's use the variable w to represent the width of the garden. We can write the following expression to represent the length: 3w - 2

Then area is calculated by multiplying the length by the width. Here that would be:

A = length • width

176 = (3w - 2 ) • w

176 = 3w² - 2w

This can be solved for w using factoring as follows:

176 = 3w² - 2w

176 - 176 = 3w² - 2w - 176

0 = 3w² - 2w - 176

Since 22 x 8 is 176, we can factor (3w² - 2w - 176): 0 = (3w + 22 ) (w - 8)

Since the width can't be a negative number, w would be 8 feet.

The length would be 3w - 2 OR 24 - 2 = 22 feet

To verify the area:

A = 22 • 88 = 176 feet ²

Answer 2

Hi Ezra,

Let's use the variable w to represent the width of the garden. We can write the following expression to represent the length: 3w - 2

Then area is calculated by multiplying the length by the width. Here that would be:

A = length • width

176 = (3w - 2 ) • w

176 = 3w² - 2w

This can be solved for w using factoring as follows:

176 = 3w² - 2w

176 - 176 = 3w² - 2w - 176

0 = 3w² - 2w - 176

Since 22 x 8 is 176, we can factor (3w² - 2w - 176): 0 = (3w + 22 ) (w - 8)

Since the width can't be a negative number, w would be 8 feet.

The length would be 3w - 2 OR 24 - 2 = 22 feet

To verify the area:

A = 22 • 88 = 176 feet ²