Question

The perimeter of a rectangle is equal to 24

. If the length is halved and the width is tripled, the new perimeter is increased by 8
. What is the length of the original rectangle?

Answer 1

The length of the original rectangle is 8.

Explanation:

If we call w the width and call L the length of the rectangle then the perimeter is calculated by the following equation:

`2w+2L=P`

In this case we know that the perimeter P is: P=24

Then:

`2w+2L=24`

If we call the new width of the rectangle w 'then

`w '= 3w`

If we call the new length of the rectangle L 'then

`L '= 0.5L`

Therefore:

`2w'+2L'=24`

`2(3w)+2(0.5L)=24+8`

`6w+L=32`

Now solve we have the following system of equations

`2w+2L=24`

`6w+L=32`

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To solve the system multiply the first equation by -3 and add it to the second equation

`-6w-6L=-72`

`6w+L=32`

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`-5L=-40\\\\L=(-40)/(-5)\\\\L=8`