SEARCH HOME Math Central Quandaries & Queries Question from Brandy, a student: Find the dimensions of a rectangle with a perimeter of 54 cm if the length is 5 less than three times the width. Hi Brandy,

Look carefully at the end of the question

the length is 5 less than three times the width

and rewrite it as

the length is 5 less than 3 × the width

but 5 less than 3 × the width is 3 × the width - 5 so the expression can be written

the length is 3 × the width - 5

Finally if I let the width be W cm and the length be L cm then I have

L = 3W - 5

You are also told that the perimeter is 54 cm. The perimeter is the distance all the way around the rectangle so

L + W + L + W = 54 or 2L + 2W = 54

Substitute L = 3W - 5 into this expression and solve for W.

Penny Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
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