# If the length of the rectangle is reduced by 1 m, and its width is increased by 1 m, then the area

**If the length of the rectangle is reduced by 1 m, and its width is increased by 1 m, then the area of the rectangle will increase by 5 m2 by how many meters is the length of the rectangle greater than its width? the answer should be 6.**

Let the length of the rectangle be D, and the width – W. Then, the reduced length will be D – 1, and the increased width will be W + 1. Let the area of the rectangle be S. Let’s write the expression for the increased area:

(D – 1) (W + 1) = S + 5

On the other hand, the area of the original rectangle would be:

D * W = S.

Substitute instead of S the product D * W in the first expression:

(D – 1) (W + 1) = D * W + 5.

Let’s expand the brackets and simplify the expression:

DW – W + D – 1 = D * W + 5;

D – W = 1 + 5;

D– W = 6.

D – W is just the difference between length and width, therefore the length is 6 m more than the width.

Answer: 6 meters.