Try the fastest way to create flashcards
Question

Solve.
The perimeter of a rectangular calculator is 36 cm36 \mathrm{~cm}. The length is 4 cm4 \mathrm{~cm} greater than the width. Find the width and the length.

Solution

Verified
Step 1
1 of 2

If we denote the length\textbf{the length} of the rectangle as l\textcolor{#c34632}{l} and its width\textbf{width} as w\textcolor{#4257b2}{w} we can determine them with the following equations:

2l+2w=362\textcolor{#c34632}{l}+2\textcolor{#4257b2}{w}=36

l=w+4\textcolor{#c34632}{l}=\textcolor{#4257b2}{w}+4

2(w+4)+2w=362w+8+2w=364w+8=364w=3684w=28w=284w=7\begin{align*} 2\cdot(\textcolor{#4257b2}{w}+4)+2\textcolor{#4257b2}{w}&=36 \tag{\textcolor{#4257b2}{Subtitution.}}\\ 2w+8+2w&=36 \tag{\textcolor{#4257b2}{Distributive law.}}\\ 4w+8&=36\\ 4w&=36-8 \tag{\textcolor{#4257b2}{Addition principle.}}\\ 4w&=28\\ w&=\frac{28}{4}\\ w&=\boxed{\textcolor{#4257b2}{7}}\\ \end{align*}

Therefore,

l=w+4=7+4=11\begin{align*} \textcolor{#c34632}{l}&=\textcolor{#4257b2}{w}+4\\ &=7+4\\ &=\boxed{\textcolor{#c34632}{11}}\\ \end{align*}

The length of the rectangle is 11\boxed{\textcolor{#c34632}{11}} cm long and its width is 7\boxed{\textcolor{#4257b2}{7}} cm long.

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Elementary and Intermediate Algebra: Concepts and Applications 6th Edition by Bittinger, Ellenbogen, Johnson

Elementary and Intermediate Algebra: Concepts and Applications

6th EditionISBN: 9780321848741 (7 more)Bittinger, Ellenbogen, Johnson
10,952 solutions
enVision Algebra 1 1st Edition by Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek

enVision Algebra 1

1st EditionISBN: 9780328931576Al Cuoco, Christine D. Thomas, Danielle Kennedy, Eric Milou, Rose Mary Zbiek
3,653 solutions
Algebra 1 4th Edition by Saxon

Algebra 1

4th EditionISBN: 9781602773011Saxon
5,377 solutions
Big Ideas Math Integrated Mathematics II 1st Edition by Boswell, Larson

Big Ideas Math Integrated Mathematics II

1st EditionISBN: 9781680330687Boswell, Larson
4,539 solutions

More related questions

1/4

1/7