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.