Question

Two rectangles are similar. The length and width of the first rectangle is 4 m by 5 m. The second rectangle is similar by a scale factor of 4. What is the area of the second rectangle in square meters

Answer 1

Answer: 320 square meters

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Step-by-step explanation:

The scale factor 4 means the dimensions of the second rectangle are 4 times larger.

The width of 4 meters bumps up to 4*4 = 16 meters.

The length of 5 meters becomes 4*5 = 20 meters.

So a 4 by 5 rectangle is similar to a 16 by 20 rectangle.

The area of the second rectangle is therefore 16*20 = 320 square meters.

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As an alternative, you can compute the area of the 4 by 5 rectangle to get 4*5 = 20. Then multiply this with 4^2 = 16 to get 16*20 = 320.

The 4^2 = 16 multiplier is the result of squaring the scale factor.

So if you know the dimensions have been multiplied by 4, then the area has been multiplied by 16.