The sum of the areas of rectangles having the same length is 220 dm². The width of the first rectangle is 4 inches

The sum of the areas of rectangles having the same length is 220 dm². The width of the first rectangle is 4 inches, and the width of the second rectangle is 3 inches larger than the width of the first. What is the length of the rectangles.

The sum of the areas of the two rectangles is 200 dm².

The lengths of the rectangles are equal. The width of the first rectangle is 4 dm, the width of the second is 3 dm wider.

The area of the rectangle S is calculated by the formula:

S = a * b, where a is the length, b is the width.

S1 = a1 * b1;

S2 = a2 * b2;

Since a1 = a2, then

S1 + S2 = a1 * (b1 + b2);

b1 = 4 dm;

b2 = b1 + 3 = 7 dm.

a1 = (S1 + S2) / (b1 + b2);

a1 = 220 / (4 + 7);

a1 = 20 dm.

The length of the rectangles is 20 dm.