Use the image to answer the question.
A composite shape is drawn with a rectangle and a square. All lines are straight and all corners are marked as right angles. The shape is made with a vertically aligned rectangle 8 yards in length and 7 yards in width. A horizontally aligned rectangle 3 yards wide and of unknown length is removed from the bottom left corner of the original rectangle. The remaining width along the bottom right is 3 yards.
Solve the following problem: A town has a swimming pool shaped as in the diagram.
What is the area of the swimming pool in square yards?
(1 point)
Responses
56 square yards
56 square yards
65 square yards
65 square yards
30 square yards
30 square yards
44 square yards
44 square yards
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To find the area of the swimming pool, we need to find the area of the original rectangle and then subtract the area of the rectangle that was removed.
The area of the original rectangle is 8 yards x 7 yards = 56 square yards.
The area of the removed rectangle is 3 yards x the unknown length, which we'll call "x". So the area of the removed rectangle is 3x square yards.
The remaining width along the bottom right is 3 yards, so the length of the removed rectangle is also 3 yards.
Therefore, we have the equation:
56 square yards - 3x square yards = 3 yards
Solving for x:
56 - 3x = 3
-3x = 3 - 56
-3x = -53
x = -53 / -3
x = 17.67
We can't have a negative length, so we'll discard this solution.
Therefore, the area of the swimming pool is 56 square yards.