Answered

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If a scale factor of 4.6 is applied to the parallelogram, what will be the perimeter of the new parallelogram?

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Answer:

The new perimeter is 4.6 times the original perimeter of the parallelogram.

Step-by-step explanation:

A parallelogram is a four-sided figure, such that the opposite sides are parallel.

So a parallelogram is defined by two measures, we can define them as the length L and the width W (W can be equal to L, as in the case of the square or the rhombus)

The perimeter of one parallelogram is then:

P = 2*L + 2*W = 2*(L + W)

If a scale factor of 4.6 is applied to the parallelogram, then all the dimensions must be multiplied by 4.6

This means that the new length is L' = 4.6*L and the new width is W' = 4.6*W

Then the new perimeter is:

P' = 2*W' + 2*L' = 2*(L' + W') = 2*(4.6*L + 4.6*W) = 4.6*[2*(L + W)]

And the thing inside brackets is equal to the original perimeter, then:

P' = 4.6*P

The new perimeter is 4.6 times the original perimeter of the parallelogram.

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