Question

Little Tikes is currently trying to plan a new sandbox for children. One sandbox they already have is a square and they are adjusting it so that one side is tripled in length and the other side is decreased by 10 meters.

The new rectangular sandbox will have an area that is so more than the original square sandbox s area. a) Write an equation that could be used to determine the length of a side of the original square sandbox.

b) Explain how your equation models the situation.

c) Determine the area, in square meters, of the new rectangular garden.

Answer 1

a. L² = 3L(L - 10)

b. The equation could be used to determine the length of a side of the original sandbox since, the areas of both sandboxes are the same.

c. 225 m²

Explanation:

a. Let L represent the length of side of the original square sandbox. Since one side of the new rectangular sandbox is increased by 3, so we have one side as 3L and the other side reduced by 10 meters, we have the other side as L - 10.

The area of the original square sandbox = L²

The area of the new rectangular sandbox = 3L(L - 10).

Since both areas are the same, we equate them.

So, L² = 3L(L - 10)

b. L² = 3L(L - 10)

The above equation could be used to determine the length of a side of the original sandbox since, the areas of both sandboxes are the same.

c. We find the area of the new rectangular garden by first solving the equation to find the length of the original sandbox.

So, L² = 3L(L - 10)

Expanding the brackets

L² = 3L² - 30L

Collecting like terms

3L² - L² = 30L

2L² = 30L

2L² - 30L = 0

2L(L - 15) = 0

2L = 0 or L - 15 = 0

L = 0 or L = 15

Since L ≠ 0 we choose L = 15 meters

So the area of the rectangular sandbox = 3L(L - 10) = 3(15)(15 -10) = 45 × 5 = 225 m²