The point of intersection of the diagonals of a rectangle is 4 cm further away from the smaller side than from the larger side of the rectangle. The perimeter of the rectangle is equal to 56cm. Find the lengths of each side of the rectangle

The given relationships can be translated to equations using L and W for the length and width of the rectangle. The distance from the center to the short side is L/2, and the distance from the center to the long side is W/2.

Setup

P = 2(L +W) . . . . . formula for the perimeter

56 = 2(L +W) . . . . . the perimeter is 56 cm

L/2 = 4 + W/2 . . . . . distance to short side is 4 cm longer

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Solution

Dividing the first equation by 2 gives ...

28 = L +W

Multiplying the second equation by 2 gives ...

L = 8 + W

Substituting for L in the first equation, we have ...

28 = (8 +W) +W . . . . . . use L=8+W

20 = 2W . . . . . . . . .subtract 8

10 = W . . . . . . . . divide by 2

L = 8 +10 = 18 . . . . . find the length

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The smaller side is 10 cm; the larger side is 18 cm.