The length of a rectangular garden is 4 more than three times the width. If the perimeter of the garden is 104 ft. What are the dimensions of the garden?

Answer 1

Hi Makayla,

Let's use the variable w to represent the width of the garden. Then we can write the following expression to represent the length of the garden: 3w + 4

Also, the perimeter (P) is equal to 2 times the length plus 2 times the width. We can write the following equation to represent the perimeter of the garden described in your problem:

104 feet = 2 • (3w + 4) + 2w

Now we can combine like terms and use inverse operations to find the value of the width, w:

104 = 6w + 8 + 2w

104 = 8w + 8

104 - 8 = 8w + 8 - 8

96 = 8w

96/8 = 8w/8

12 = w

The width is 12 feet. The length will be 3 • 12 + 4 = 36 + 4 = 40 feet

To verify: 2 • 40 + 2 • 12 = 80 + 24 = 104 feet

Hope this helps Makayla. Let me know if you need any lessons or have other questions.