Question

A rectangle is dilated by a factor of 1/5. The area of the new rectangle is 4 square yards. What could be the dimensions of the original rectangle?

Answer 1

10×10

On edge

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Answer 2

We know that a rectangle is dilated by a factor of 1/5 which means that the area of a rectangle is dilated by a factor of 1/25. I get 1/25 because each side was dilated by a factor of 1/5, so I just need to take 1/5×1/5=1/25 as the factor of area if rectangle.
Then, the new rectangle is 4 square yards, so we just need to find the area of the old or pre-rectangle. Furthermore, we know that the pre-rectangle is 25 times bigger than the new rectangle based on what we did above, so the area of the pre-rectangle is:
4×25=100 square yards.
However, the question asked us to find the possibility dimension of the original images.
Area of the rectangle=
length× width
100 square yards
length=20 yards, width=5 yards
length=100 yards, width=1 yard
length=25 yards, width=4 yards. Hope it help!