The ratio of the length to the width of a rectangle is 7:4. If its perimeter is 88 cm, what is its area?
448 cm²
Let the length and width share the ratio 7 : 4, so write length \(= 7x\) cm and width \(= 4x\) cm, where \(x\) is a common multiplier.
The perimeter of a rectangle is \(2(\text{length} + \text{width})\), so \(2(7x + 4x) = 88\).
This gives \(2\times 11x = 22x = 88\), hence \(x = \dfrac{88}{22} = 4\).
Therefore length \(= 7\times 4 = 28\) cm and width \(= 4\times 4 = 16\) cm.
Area of a rectangle \(= \text{length}\times \text{width} = 28\times 16\).
\(28\times 16 = 448\), so the area is 448 square centimetres.
Key concept: use the perimeter formula to fix the scale factor first, then apply the area formula.
Hence the area of the rectangle is 448 cm².
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