# 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

### The Absolute Best Book to challenge your Smart Student!

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

The Best Books to Ace AlgebraOriginal price was: $29.99.$14.99Current price is: $14.99.Original price was: $29.99.$14.99Current price is: $14.99.Satisfied 1 StudentsOriginal price was: $24.99.$14.99Current price is: $14.99.Satisfied 92 StudentsOriginal price was: $24.99.$15.99Current price is: $15.99.Satisfied 125 Students

## Related to This Article

### More math articles

- How to Do Division Using Repeated Subtraction
- Algebra Puzzle – Challenge 54
- Full-Length 7th Grade GMAS Math Practice Test-Answers and Explanations
- How to Change Base Formula for Logarithms?
- How to Graph Transformation on the Coordinate Plane: Dilation?
- 7th Grade ACT Aspire Math FREE Sample Practice Questions
- The Ultimate 7th Grade MAP Math Course (+FREE Worksheets)
- How to Master Polynomial Functions: A Comprehensive Guide to Understanding and Solving Complex Zeros
- 10 Most Common 5th Grade PSSA Math Questions
- Top 10 Tips to Create a CHSPE Math Study Plan

## What people say about "Geometry Puzzle – Challenge 68 - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.