A square is drawn with a scale factor of 1-2 with original square- What is the ratio of their areas-

The correct option is D 1/4Scale factor is defined in the following way: Scale factor =Length of reduced side/length of original side For example: Given, Scal ...

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Standard VIII

Mathematics

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A square is d...

Question

A square is drawn with a scale factor of $\frac{1}{2}$ with original square. What is the ratio of their areas?

\frac{1}{4}

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\frac{1}{2}

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\frac{1}{16}

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\frac{1}{2}

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Solution

The correct option is A $\frac{1}{4}$
Scale factor is defined in the following way:
Scale factor $= \frac{L e n g t h o f r e d u c e d s i d e}{l e n g t h o f o r i g i n a l s i d e}$
For example:
Given,
Scale factor $= \frac{L e n g t h o f r e d u c e d s i d e}{l e n g t h o f o r i g i n a l s i d e} = \frac{1}{2}$

Ratio of areas $= \frac{(L e n g t h o f r e d u c e d s i d e)^{2}}{(L e n g t h o f o r i g i n a l s i d e)^{2}} = (S c a l e f a c t o r)^{2} = (\frac{1}{2})^{2} = \frac{1}{4}$

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Question 3

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