# Geometry Puzzle – Challenge 68

This is a great geometry and algebra related puzzle to help you or your students enjoy learning math in a fun way!

## 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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The correct answer is E.

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

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