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# A dance floor is made from square wooden tiles with a side length of 1 foot. The floor can be laid out as a square or as a rectangle. The width of the rectangular floor is 10 feet less than the width of the square floor, and its length is 15 feet greater than the length of the square floor. The perimeter of the rectangular dance floor is 130 feet. What are the length and width of the dance floor? Explain your reasoning.

Solution

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The formula for the perimeter of a rectangular is given by

$\color{#4257b2}P=2w+2l$

We have: $P=130$ feet.

\begin{align*} P&=2w+2l\tag{Subtitute 130 for P}\\ 130&=2w+2l\tag{Subtitute the expression from (a) part for l}\\ 130&=2w+2\cdot (w+25)\tag{Use the distributive property}\\ 130&=2w+2w+2\cdot 25\tag{Multiply 25 by 2 adn add 2w and 2w}\\ 130&=4w+50\tag{Subtract 50 from both sides}\\ 80&=4w\tag{Divide by 4}\\ \boxed{w=20} \end{align*}

Therefore, the width is $20$ feet.

Subtitute $20$ for $w$ in expression for $l$:

$l=25+w=25+20=\boxed{45}$

Therefore, the length is $45$ feet.

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