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Annuli, sectors and area constraints
Free examples and worked answers. No account needed.
Practise the method.
Annuli, sectors and area constraints
Annuli, sectors and area constraints
Example 1
A 4m by 8m rectangular garden has a path of uniform width x around its outside. The path area is 64m2. Find x in metres.
Uniform borderDiagram not to scaleShow worked answer
Answer: 2
- The outer rectangle is (4+2x) by (8+2x).
- Subtract 32, set equal to 64, and solve the quadratic.
- The positive root is 2.
Example 2
A rectangle has perimeter 34cm and area 66cm2. Find its longer side, in cm.
RectangleDiagram not to scaleShow worked answer
Answer: 11
- The sides add to 17 and multiply to 66.
- They are 6 and 11cm;
- the longer side is 11cm.
Example 3
A 6m by 12m rectangular garden has a path of uniform width x around its outside. The path area is 88m2. Find x in metres.
Uniform borderDiagram not to scaleShow worked answer
Answer: 2
- The outer rectangle is (6+2x) by (12+2x).
- Subtract 72, set equal to 88, and solve the quadratic.
- The positive root is 2.
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