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Mathematics

A rectangle having an area of 60 cm2 is transformed under enlargement about a point in space. If the area of its image is 135 cm2, find the scale factor of the enlargement.

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Answer

Let scale factor be k.

We know that,

Area of the image = k2 × (Area of the rectangle)

⇒135=k2×60⇒k2=13560⇒k2=94⇒k=94⇒k=32=1.5\Rightarrow 135 = k^2 \times 60 \\[1em] \Rightarrow k^2 = \dfrac{135}{60} \\[1em] \Rightarrow k^2 = \dfrac{9}{4} \\[1em] \Rightarrow k = \sqrt{\dfrac{9}{4}} \\[1em] \Rightarrow k = \dfrac{3}{2} = 1.5

Hence, scale factor of enlargement = 1.5

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