Mark’s vegetable garden is in the shape of a rectangle, and he can enclose it with 96 feet of fencing. if the length of his garden is 16 feet more than 3 times the width, what are the dimensions of the garden?

length = 40 ft; width = 8 ft

Step-by-step explanation:

Let the width = x.

The fence has to go around the entire perimeter of the garden.

A rectangle has 4 sides: 2 lengths and 2 widths.

The perimeter is the sum of the lengths of the 4 sides.

perimeter = length + length + width + width

We are told the perimeter is 96 ft, so we have:

length + length + width + width = 96

Above, we let the width = x.

The length of the rectangle is 16 ft more than 3 times the width.

Since the width is x, the length is 3 times the width, 3x, plus 16, so the width is 3x + 16. We substitute x for each width and 3x + 16 for each length.

length + length + width + width = 96

3x + 16 + 3x + 16 + x + x = 96

Add like terms on the left side.

3x + 3x + x + x + 16 + 16 = 96

8x + 32 = 96

Subtract 32 from both sides.

8x = 64

Divide both sides by 8.

x = 8

Since we let the width = x, now we know the width is 8 ft.

The length is 16 ft more than 3 times the width.

length = 3x + 16 = 3(8) + 16 = 24 + 16 = 40

length = 40 ft; width = 8 ft

Check: 40 ft is indeed 16 more than 3 times 8 since 3(8) + 16 = 40.

Also, 2 lengths of 40 ft and 2 widths of 8 ft do add to 96 ft.

Our answer is correct.

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