Question

A rectangle with an area of 78 units^2 is the image of a rectangle that was dilated by a
scale factor of 3. Find the area of the preimage, the original rectangle, before its
dilation. Round your answer to the nearest tenth, if necessary.

Answer 1

The area of the preimage, the original rectangle before its dilation is 8.7 units².

How to determine the pre image of a dilated shape

area of the dilated image = 78 units²

Therefore,

a₂ = a₁k²

where

a₂ = image area of the dilated rectangle

a₁ = pre image of the dilated rectangle

k = scale factor

Therefore,

a₂ = 78 units²

a₁ = ?

k = 3

78 = a₁ × 3²

divide both sides by 3

a₁ = 78 / 9

a₁ = 8.7 units²

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