Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The length of a rectangle is 1 meter less than its width. The area of the rectangle is 42 square meters. Find the dimensions of the rectangle.

$4$ . The length of a rectangle is $1$ meter less than its width. The area of the rectangle is $42$ square meters. Find the dimensions of the rectangle.

View step-by-step help

View step-by-step help

Area and perimeter: word problems

Full solution

Q.

4

. The length of a rectangle is

1

meter less than its width. The area of the rectangle is

42

square meters. Find the dimensions of the rectangle.

Define Variables: Let's call the width of the rectangle $w$ and the length $l$ . We know that the length is $1$ meter less than the width, so we can write $l = w - 1$ .
Calculate Area: The area of the rectangle is given by the formula $\text{Area} = \text{length} \times \text{width}$ , which is $42 = l \times w$ . Substituting $l$ with $w - 1$ , we get $42 = (w - 1) \times w$ .
Solve Quadratic Equation: Now we need to solve the quadratic equation $42 = w^2 - w$ . Moving all terms to one side, we get $w^2 - w - 42 = 0$ .
Factorize Equation: To solve the quadratic equation, we can factor it. We're looking for two numbers that multiply to $-42$ and add up to $-1$ . Those numbers are $-7$ and $6$ , so we can write $(w - 7)(w + 6) = 0$ .
Find Width: Setting each factor equal to zero gives us $w - 7 = 0$ or $w + 6 = 0$ . Solving for $w$ gives us $w = 7$ or $w = -6$ . Since a width can't be negative, we discard $w = -6$ .
Find Length: Now that we have the width $w = 7$ , we can find the length by substituting $w$ into $l = w - 1$ . So $l = 7 - 1 = 6$ .

More problems from Area and perimeter: word problems

Question

A square window has a perimeter of \(136\) inches. How long is each side?

\newline

\_\_\_\_\_

Posted 2 months ago

Question

What is the greatest possible error for a measurement of

2

\newline

\_\_\_

Posted 3 months ago

Question

What is the percent error for a measurement of

5

?

\newline

If needed, round your answer to the nearest hundredth of a percent.

\newline

\newline

Posted 2 months ago

Question

Which measurement is more precise?

\newline

\newline

29.4

\newline

31

Posted 3 months ago

Question

A new dictionary in the shape of a rectangular prism will have a thickness of

3

inches (in). The volume of the dictionary will be

216 \mathrm{in}^{3}

. What must be the area of the front cover, a face perpendicular to the thickness, in square inches?

Posted 4 months ago

Question

Sako's garden is

6

yards long. What is the length of his garden in feet?

Posted 3 months ago

Question

Avery is designing a large rectangular sign. They want the sign to have an area of

2\,\text{m}^2

\frac{4}{5}\,\text{m}

. How tall should the sign be?

Posted 3 days ago

Question

Find the monthly payment for a

30

100000

4\%

Posted 3 months ago

Question

Gabriel is designing a rectangular planter box for their garden. It needs to cover an area of

15 \frac{1}{2} \text{ m}^2

. Gabriel wants it to be

7 \frac{3}{4}

long. How wide does the planter box need to be?

Posted 3 months ago

Question

An electrician plans to install solar panels on a rectangular section of roof with an area of

180\text{m}^2

. This width of this section of roof is

7\frac{1}{5}

Posted 3 months ago