Chapter 12: Q28. (page 745)

A piece of wire 42 centimeters long is bent into the shape of a rectangle with a width that is twice its length. Find the dimensions of the rectangle.
A. 5cm, 12cm
B. 7cm, 14cm
C. 9cm, 16cm
D. 11cm, 18cm

Short Answer

Expert verified

Option Bis correct. The dimensions of the rectangle are 7cm, 14cm.

Step by step solution

Step 1. Write the formula for perimeter of rectangle.

Perimeter of a rectangle is given by:

$Perimeter = 2 (l + w)$

where $l$ is the length and $w$ is the width of a rectangle.

Step 2. Form the equation.

Let length be $x$ cm.

The width of the rectangle is twice its length.

Therefore, width $= 2 x$ cm

The length of the wire is 42 cm.

Therefore, perimeter cm

The equation can be written as:

$2 (l + w) = Perimeter 2 (l + w) = 42$

Step 3. Solve the equation.

The equation can be solved as follows:

$\begin{matrix} 2 (l + w) = 42 \\ 2 (x + 2 x) = 42 \\ 2 x + 4 x = 42 \end{matrix}$

localid="1648196637308" $\begin{matrix} 6 x = 42 \\ \frac{6 x}{6} = \frac{42}{6} \\ x = 7 \end{matrix}$

Therefore, the dimensions are $x = 7 c m and 2 x = 14 c m .$

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A piece of wire 42 centimeters long is bent into the shape of a rectangle with a width that is twice its length. Find the dimensions of the rectangle.
A. 5cm, 12cm
B. 7cm, 14cm
C. 9cm, 16cm
D. 11cm, 18cm

Short Answer

Step by step solution

Step 1. Write the formula for perimeter of rectangle.

Step 2. Form the equation.

Step 3. Solve the equation.

One App. One Place for Learning.

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A piece of wire 42 centimeters long is bent into the shape of a rectangle with a width that is twice its length. Find the dimensions of the rectangle.A. 5cm, 12cmB. 7cm, 14cmC. 9cm, 16cmD. 11cm, 18cm

Short Answer

Step by step solution

Step 1. Write the formula for perimeter of rectangle.

Step 2. Form the equation.

Step 3. Solve the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

A piece of wire 42 centimeters long is bent into the shape of a rectangle with a width that is twice its length. Find the dimensions of the rectangle.
A. 5cm, 12cm
B. 7cm, 14cm
C. 9cm, 16cm
D. 11cm, 18cm