Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The perimeter of a rectangular piece of metal is $150$ centimeters. The piece is $26$ centimeters wide. How long is it? $\newline$ _____ centimeters

View step-by-step help

View step-by-step help

Area and perimeter: word problems

Full solution

Q. The perimeter of a rectangular piece of metal is

150

centimeters. The piece is

26

centimeters wide. How long is it?

\newline

_____ centimeters

Identify formula: Identify the formula for the perimeter of a rectangle. $\newline$ The formula for the perimeter of a rectangle is $P = 2l + 2w$ , where $P$ is the perimeter, $l$ is the length, and $w$ is the width.
Plug in values: Plug in the values of $P$ and $w$ into the formula. $\newline$ Given $P = 150$ centimeters and $w = 26$ centimeters, we can substitute these values into the formula to get $150 = 2l + 2(26)$ .
Simplify equation: Simplify the equation by performing the multiplication. $150 = 2l + 52$
Isolate term with l: Isolate the term with $l$ by subtracting $52$ from both sides of the equation. $\newline$ $150 - 52 = 2l$ $\newline$ $98 = 2l$
Solve for l: Solve for l by dividing both sides of the equation by $2$ . $\newline$ $\frac{98}{2} = l$ $\newline$ $49 = l$
Check solution: Check the solution by plugging the value of $l$ back into the original perimeter formula. $P = 2l + 2w$ $150 = 2(49) + 2(26)$ $150 = 98 + 52$ $150 = 150$ The solution checks out.

More problems from Area and perimeter: word problems

Question

Skyler climbs a watchtower to guard against forest fires.

\newline

R(h)=\sqrt{13h}

gives the distance, in kilometers, that Skyler can see when their eyes are

h

meters above the ground.

\newline

A(d)=\pi d^{2}

gives the area, in square kilometers, that Skyler can guard when they can see a distance of

d

\newline

Which expression models the area Skyler can guard when their eyes are

h

meters above the ground?

\newline

1

\newline

13\pi h

\newline

13\pi h^{2}

\newline

\sqrt{13\pi h^{2}}

\newline

169\pi h^{2}

Posted 8 months ago

Question

After the outbreak of a mysterious disease, the average wait time at a hospital increased by

70\%

. Before the outbreak, the average wait time at the hospital was

m

\newline

Which of the following expressions could represent the average wait time at the hospital after the outbreak?

\newline

2

\newline

0.7m

\newline

\frac{170}{100}m

\newline

m+70

\newline

m+0.7

\newline

1.7m

Posted 7 months ago

Question

The radius of a semicircle is

3

yards. What is the semicircle's area?

\newline

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

Posted 8 months ago

Question

\newline

A man has bent a circular wire of radius

49\text{cm}

to form a square. Find the sides of a square.

\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

Posted 8 months ago

Question

A quarter is worth

\$0.25

and a half dollar is worth

\$0.50

\newline

a. A quarter has a diameter of

\frac{15}{16}

inch and a height of

\frac{1}{16}

inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.

\newline

b. A half dollar has a diameter of

\frac{9}{8}

inches and a height of

\frac{3}{32}

inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.

Posted 8 months ago

Question

The hypotenuse of a right triangle measures

17 \mathrm{~cm}

and one of its legs measures

8 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 8 months ago

Question

One of the legs of a right triangle measures

15 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 9 months ago

Question

One of the legs of a right triangle measures

8 \mathrm{~cm}

and the other leg measures

15 \mathrm{~cm}

. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 8 months ago

Question

Find the volume of a right circular cone that has a height of

7.4 \mathrm{~cm}

and a base with a radius of

8.1 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

\mathrm{cm}^{3}

Posted 9 months ago

Question

Find the volume of a right circular cone that has a height of

13.3 \mathrm{ft}

and a base with a diameter of

9.4 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

\mathrm{ft}^{3}

Posted 9 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant