A rectangle with perimeter #70# feet has area #300# square feet. What are its dimensions?

1 Answer
Dec 3, 2016

Answer:

#15 xx 20# feet

Explanation:

Let the length of one side be #x#.

Going round the rectangle, the other sides are of lengths:

#35 - x#

#x#

#35 - x#

The area of the rectangle is:

#300 = x(35-x)#

So essentially we are looking for a pair of factors of #300# which sum to #35#.

Since #300# and #35# are both divisible by #5#, the pair we are looking for must both be divisible by #5# too.

So the pairs of factors we need to consider are:

#5 * 60" "# with #" "5+60 = 65#

#10 * 30" "# with #" "10+30 = 40#

#color(blue)(15 * 20)" "# with #" "color(blue)(15+20 = 35)#