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The perimeter of a rectangular floor is $90$ feet. How do you find the dimensions of the floor if the length is twice the width?

Answer
VerifiedVerified
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Hint: Start by mentioning the definition of perimeter of a rectangle. Then we will mention the formula for the perimeter of the rectangle and substitute values in the formula. Then finally evaluate the conditions and solve for the dimensions of the rectangle.

Complete step by step answer:
First we will start off by mentioning the definition of perimeter. So, the perimeter is a path that surrounds a two-dimensional shape. This term may be used either for the path, or its length in one dimension.
Now, the perimeter of a rectangle is given by, $2(l + b)$.
Now let us consider the width of the rectangle as $x$ and the length of the rectangle as $2x$.
And according to the question, the perimeter of the rectangle is $90$ feet.
So, now substitute the above values in the formula of the perimeter of the rectangle.
$90 = 2(l + b) $
$90 = 2(2x + x)$
$90 = 2(3x) $
$90 = 6x $
$ x = 15 $
Hence, the value of $x$ is $15$ . That is the width of the rectangle is $15$ feet.
Now we will evaluate the length of the rectangle.
$= 2x $
$= 2 \times 15 $
$= 30 $
Hence, the length of the rectangle is $30$ feet.
Therefore, the dimensions of the rectangle are $30$ feet and $15$ feet.

Note: While mentioning the definition, make sure to mention the terms properly. Reduce the terms by factorisation. While choosing any variable, for any unknown term, choose according to the conditions.