The scale drawing of a rectangular room will be enlarged by a scale factor of 4 to create the actual room. The actual area of the room will be 150 square feet. Which expression finds the area of the scale drawing? StartFraction 4 squared over 150 squared EndFraction StartFraction 4 squared over 150 EndFraction StartFraction 150 over 4 squared EndFraction StartFraction 150 over 4 EndFraction
Question
The scale drawing of a rectangular room will be enlarged by a scale factor of 4 to create the actual room. The actual area of the room will be 150 square feet. Which expression finds the area of the scale drawing? StartFraction 4 squared over 150 squared EndFraction StartFraction 4 squared over 150 EndFraction StartFraction 150 over 4 squared EndFraction StartFraction 150 over 4 EndFraction
Solution
The correct expression to find the area of the scale drawing is StartFraction 150 over 4 squared EndFraction.
Here's why:
The scale factor is the ratio of the lengths of corresponding sides in the actual room and the scale drawing. If the scale factor is 4, it means that each side of the actual room is 4 times longer than the corresponding side in the scale drawing.
The area of a rectangle is found by multiplying the lengths of its sides. Therefore, the area of the actual room is (4 times the length of the scale drawing) times (4 times the width of the scale drawing), which is 16 times the area of the scale drawing (since 4 squared is 16).
So, if the actual area of the room is 150 square feet, the area of the scale drawing is 150 divided by 16, or StartFraction 150 over 4 squared EndFraction.
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