Geometry Puzzle – Challenge 68

Challenge:

The sum of three sides of a rectangular is 63. The sum of three sides of the same rectangle is 51. What is the area of the rectangle?

A- 168

B- 169

C- 240

D- 300

E- 325

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A rectangle has two widths and two lengths. Therefore, the perimeter equals: 2 × (width + length)
Since, the sum of three sides of a rectangular is 63 and the sum of other three sides of the rectangle is 51. Let’s assume the width is smaller the length. Let W be the width and L be the length. Therefore:
2W + L = 51 and W + 2 L = 63
Solve the system of equations:
2W + L = 51 → L = 51 – 2W
W + 2 L = 63 → W + 2 (51 – 2W) = 63→ W + 102 – 4W = 63 →
W = 13 and W + 2 L = 63 → 13 + 2L = 63 → 2L = 50 → L = 25
The area of the rectangle is:
W × L = 13 × 25 = 325