Infer dimensions before comparing and combining areas

Answer: 20

1. The opening area is 112−96=16.
2. Solve (14−2x)(8−2x)=16;
3. the valid width is x=3m(the other root makes a dimension non-positive).
4. The opening is 8 by 2
5. its perimeter is 20m.

Answer: 112.5

1. The side lengths add to 23 and multiply to 126
2. they are 9 and 14cm.
3. The removed area is ½ ×9×3=13.5.
4. Remaining area =126−13.5=112.5cm2.

Answer: 32

1. The opening area is 140−80=60.
2. Solve (10−2x)(14−2x)=60;
3. the valid width is x=2m(the other root makes a dimension non-positive).
4. The opening is 6 by 10
5. its perimeter is 32m.