A rectangle 12

A rectangle has a width of 7.2 cm shorter than its length. The perimeter of this rectangle is 22.8 cm. Write the width-to-length ratio of this rectangle in the simplest form and show how you solve the problem.

Correct answer:

r =  7:31

Step-by-step explanation:

$$\begin{gathered} w=l-7.2 \\ 22.8=2w+2l \\ w=l-7.2 \\ 22.8=2\cdot w+2\cdot l \\ l-w=7.2 \\ 2l+2w=22.8 \\ Pivot:Row1\leftrightarrow Row2 \\ 2l+2w=22.8 \\ l-w=7.2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2l+2w=22.8 \\ -2w=-4.2 \\ w=\frac{-4.2}{-2}=2.1 \\ l=\frac{22.8-2w}{2}=\frac{22.8-2\cdot 2.1}{2}=9.3 \\ l=\frac{93}{10}=9.3 \\ w=\frac{21}{10}=2.1 \\ r=w:l=2.1:9.3=7:31\approx 0.2258=7:31 \end{gathered}$$

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