If each side of a rhombus is doubled, how much will its area increase by:

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1.5 times

2 times

3 times

4 times

answer is D.

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Detailed Solution

Given, a rhombus whose each side is doubled.
A rhombus is a parallelogram with all sides are equal.
Next, the area of a rhombus is given by the product of its base and its height.
Now, if each side of a rhombus is doubled, then its altitude or height will automatically be doubled.
So, assuming the base length of a rhombus to be ‘b’ and its altitude as ‘h’, we have the original area as

b × h

.
Now, when both the base length is doubled, then the base will be 2b and the new altitude will also be 2h.
Then the area of the new rhombus will be

2 b × 2 h = 4 (b × h)

.
So, we can observe that the new area of the rhombus is four times its original area.
So, the area of the rhombus increases by 4 times.
Hence, the correct option is (4).

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