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Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset Vaia Explanations$ Math

Student Edition · 227 pages

ISBN: 9780395977279

Chapter 11: Q31. (page 427)

A rectangle having area $392 m^{2}$ is twice as long as it is wide. Find its dimensions.

Short Answer

Expert verified

The dimensions are $28 m \times 14 m$ .

Step by step solution

01

Step 1. Given information.

Area of the rectangle $A = 392 m^{2}$ .

Length is twice as its width.

02

Step 2. Concept Used.

If b is the width of the rectangle and i is the length of the rectangle.

Then, the area of the rectangle is $A = l \times b$

03

Step 3. Let’s calculate the dimensions and area of the rectangle.

According to the given situation, length is twice as its width i.e.

$l = 2 b$

The area of the rectangle;

$\begin{matrix} A = l \times b \\ 392 = (2 b) \times b \\ 392 = 2 b^{2} \\ b^{2} = \frac{392}{2} \\ b^{2} = 196 \\ b = \sqrt{196} \\ b = 14 m \end{matrix}$

Let’s calculate the length of the rectangle.

$\begin{matrix} l = 2 (14) \\ = 28 m \end{matrix}$

Therefore, the dimensions of the rectangle is $28 m \times 14 m$ .

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Most popular questions from this chapter

A path2mwide surroundings a rectangular garden 20mlong and 12mwide. Find the area of the path.

Give two formulas that can be used to find the area of a rhombus. (Hint: Every rhombus is also a _______).

a. Use the diagram at the right. Find the area of $▱ P Q R S$ .

b. Use the diagram at the right. Find the area of $△ P S R$ .

c. Use the diagram at the right. Find the area of $△ O S R$ . (Hint: Refer to $△ P S R$ and use Exercise28).

d. Use the diagram at the right. What is the area of $△ P S O$ ?

e. Use the diagram at the right. What must the area of $△ P O Q$ be? Why? What must the area of $△ O Q R$ be?

f. Use the diagram at the right. State what you have shown in parts (a)-(e) about how the diagonals of a parallelogram divide the parallelogram.

The base of a rectangle is $(a + 3)$ and height $(a - 3)$ . What is the area and perimeter of the rectangle?

The base of a rectangle is $8.2 c m$ and height 4cm.What is the area?

See all solutions

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