## Related questions with answers

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

VerifiedThe 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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