Annuli, sectors and area constraints

Answer: 2

1. The outer rectangle is (4+2x) by (8+2x).
2. Subtract 32, set equal to 64, and solve the quadratic.
3. The positive root is 2.

Answer: 11

1. The sides add to 17 and multiply to 66.
2. They are 6 and 11cm;
3. the longer side is 11cm.

Answer: 2

1. The outer rectangle is (6+2x) by (12+2x).
2. Subtract 72, set equal to 88, and solve the quadratic.
3. The positive root is 2.