The playing surface in the game of curling is a rectangular sheet of ice with an area of about 225m^2. The width is about 40 m less than the length. How do you find the approximate dimensions of the playing surface?

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Answer 1 · 2016-05-22T02:50:30

Express width in terms of length, then substitute and solve to arrive at the dimensions of $L=45m$ and $W=5m$

We start with the formula for a rectangle:

$A=LW$

We're given the area and we know that the width is 40m less than the length. Let's write the relationship between L and W down:

$W=L-40$

And now we can solve $A=LW$ :

$225=L(L-40)$

$225=L^2-40L$

I'm going to subtract $L^2-40L$ from both sides, then multiply by $-1$ so that $L^2$ is positive:

$L^2-40L-225=0$

Now let's factor and solve for L:

$(L-45)(L+5)=0$

$(L-45)=0$
$L=45$

and

$(L+5)=0$
$L=-5$

So L = 45. Now let's solve for W:

$W=45-40=5$

So the dimensions are $L=45m$ and $W=5m$