Geometry Puzzle – Challenge 72

Challenge:

The length of a rectangle is three times its width. What is the ratio of its width to its perimeter?

A- 1: 4

B- 1: 6

C- 1: 8

D- 2: 9

E- 3: 10

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Let x be the width of the rectangle. So, the length of the rectangle is 3x.
Perimeter of a rectangle = 2 × Width + 2 × Length =
2x + 2 (3x) = 8x
The ratio of its width to its perimeter is 1 to 8.

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Frequently Asked Questions

How do you find the ratio of length to width of a rectangle?

Write the length over the width and simplify. A rectangle 15 cm long and 5 cm wide has a length-to-width ratio of 15:5 = 3:1. In this puzzle that ratio is given (length is three times width), and the question asks for width to perimeter instead, which works out to 1:8 because the perimeter is 2(3x + x) = 8x.

How do you write a ratio of length to width?

Put the length first and the width second, separated by a colon or written as a fraction: length:width or length/width. Then divide both parts by their greatest common factor. For a rectangle 12 m by 8 m, the ratio is 12:8, which simplifies to 3:2. Order matters, so 3:2 (length to width) is not the same as 2:3.

How do you calculate the length to width ratio?

Divide the length by the width. If a rectangle is 27 inches long and 9 inches wide, 27 ÷ 9 = 3, so the ratio is 3:1, just like the rectangle in this challenge. When the result isn’t a whole number, keep it as a simplified fraction; 10 by 4 gives 10/4 = 5/2, or 5:2.

What is the area to perimeter ratio of a rectangle?

Divide the area by the perimeter: (L × W) ÷ 2(L + W). Unlike the width-to-perimeter ratio in this puzzle, it depends on the rectangle’s size. For a rectangle with length 3x and width x, the area is 3x² and the perimeter is 8x, so the ratio is 3x/8. With x = 5, that is 75 ÷ 40 = 15/8.

How do you find the dimensions of a rectangle from its perimeter?

You need the perimeter plus one more fact, such as how the length compares to the width. Suppose the perimeter is 40 cm and the length is three times the width. Then 2(3x + x) = 8x = 40, so x = 5. The width is 5 cm and the length is 15 cm. Check: 2(15 + 5) = 40.

Related Lessons You May Like

• How to find the area of rectangles
• How to find the perimeter of rectangles
• How to solve angles and angle measure
• How to solve percent of change
• How to find volume and surface area of cubes

If your student enjoys puzzles like this, Geometry for Beginners works the same kinds of relationships inside a full curriculum. Pre-Algebra for Beginners covers the algebraic foundations.