Question

Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden’s width to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Answer 1

If x is the length of the square tomato patch, then the width of the tomato patch is also x, since it is a square.

According to the problem, the length of the rectangular vegetable garden must exceed three times the length of the tomato patch by 2 feet, so the length of the garden is:

3x + 2

The width of the rectangular vegetable garden must exceed the width of the tomato patch by 5 feet, so the width of the garden is:

x + 5

To find the area of the garden, we multiply its length by its width:

Area of garden = length x width

Area of garden = (3x + 2)(x + 5)

To find the area of the tomato patch, we note that it is a square with side length x, so its area is:

Area of tomato patch = x²

Therefore, the area of the vegetable garden that is not taken up by the tomato patch is:

(3x + 2)(x + 5) - x²

And the total area of the vegetable garden, including the tomato patch, is:

x² + (3x + 2)(x + 5)

Simplifying:

x² + (3x² + 17x + 10)

4x² + 17x + 10

So the total area of the garden is 4x² + 17x + 10 square feet.