Math CentralQuandaries & Queries


Question from meg, a student:

if a rectangle has a length that is 3cm less than 4 times its width and its perimeter is 19cm, what are the dimension?

Hi Meg,

The two quantities you don't know are the length and the width of the triangle so let $L$ be the length in centimeters and $W$ be the width. The first restriction is that "a length that is 3cm less than 4 times its width". If $W$ is the width what is 4 times the width? What is 3 cm less than this? Set this equal to the length and you have an equation relating the length and the width.

The second restriction is that "its perimeter is 19cm". The perimeter is the distance around the rectangle. What is this in terms of $L$ and $W?$ Set this equal to 19 to obtain a second equation relating $L$ and $W.$ Substitute $L$ from the first equation into the second and solve for $W.$ Use this value of $W$ and the first equation to solve for $L.$


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