The perimeter is 46 meters and its length is 2 meters more than twice its width. What is the length?

Friday, July 22, 2011

In this problem, the length is compared to the width of the rectangle. So let's assign a variable that represents the width of the rectangle.

Let the width be w.

$\displaystyle{w}{i}{\left.{d}{t}\right.}{h}={w}$

Since the length is 2 meters more than twice its width, the expression that represent it is:

$\displaystyle{l}{e}{n}{g{{t}}}{h}={2}{w}+{2}$

Then, plug-in the length and width to the formula of perimeter of rectangle.

$\displaystyle{P}={2}\cdot{l}{e}{n}{g{{t}}}{h}+{2}\cdot{w}{i}{\left.{d}{t}\right.}{h}$

$\displaystyle{P}={2}{\left({2}{w}+{2}\right)}+{2}\cdot{w}$

Plug-in too the given perimeter of the rectangle.

$\displaystyle{46}={2}{\left({2}{w}+{2}\right)}+{2}\cdot{w}$

Then, solve for w.

$\displaystyle{46}={4}{w}+{4}+{2}{w}$

$\displaystyle{46}={6}{w}+{4}$

$\displaystyle{42}={6}{w}$

$\displaystyle{7}={w}$

So, the width of the rectangle is 7 meters.

Then, plug-in the value of w to the expression that represents the length.

$\displaystyle{l}{e}{n}{g{{t}}}{h}={2}{w}+{2}$

$\displaystyle{l}{e}{n}{g{{t}}}{h}={2}{\left({7}\right)}+{2}$

$\displaystyle{l}{e}{n}{g{{t}}}{h}={14}+{2}$

$\displaystyle{l}{e}{n}{g{{t}}}{h}={16}$

Therefore, the length of the rectangle is 16 meters.

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