the ratio of the lengths of the sides is 2:7

The sides are 2 times some base value and 7 times the base value. The

perimeter is 2 times the short side plus 2 times the long side.

(2 * 2x) + (2 * 7x) = 36

4x + 14x = 36

18x = 36

x = 2

The short sides are 2 * 2 = 4

The long sides are 2 * 7 = 14

Let L be the length and W the width of the rectangle. We know that:

1.) W/L = 2/7 or

W = (2/7)*L

2.) 36 = 2*W + 2*L

Substituting (2/7)*L for W in equation 2.) we have:

36 = 2*(2/7)*L + 2*L

36 = (4/7)*L + (14/7)*L

36 = (18/7)*L

Multiply both sides by 7/18:

36*(7/18) = 1*L

14 = L

Calculate W = (2/7)*L

W = (2/7)*14

W = 4

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