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?

1 Answer

Answer:

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

Explanation:

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#