Question

A rectangle is one-fifth as tall as it is long. If its height is reduced to one-half of its current height, what is the ratio of the new rectangle's perimeter to the original rectangle's perimeter?

Answer 1

So the original rectangle has length L and height H

Its perimeter is 2(L + H)

The new rectangle has length L and height (1/2) H

Its perimeter is 2(L + 1/2 H) = 2L + H

The ratio is (2L + H) / (2L + 2H) = (2 L/H + 1) / (2 L/H + 2)


Since L/H = 5, then this ratio is (2(5)+1) / (2(5) + 2) = 11/12

Answer 2

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