What are the dimensions of a square that encloses the same area as a rectangle that is two miles long and one mile wide?

1 Answer
The Lonely Donut
Nov 23, 2017

#s = sqrt(2)# miles

Explanation:

The dimensions of the rectangle are:

#l = 2#
#w = 1#

Now we use the area formula.

#A = lw #
#A = (2)(1) #
#A = 2#

The question asks for the dimensions of a square that has the same area as the rectangle. So the area of the square must also be #2#.

Now we know that the formula for area for a square is #A = s^2#, so we could just plug in the area and solve for #s#.

#A = s^2#
#(2) = s^2#
#+-sqrt2 = sqrt(s^2)#
#s=+-sqrt2#

Your solution set would be:

#s = -sqrt2#
#s=sqrt2#

However, since this is a real-life problem, we know that a side of a square cannot be negative. We can eliminate the negative solution and we have our answer.

#s=sqrt2# miles

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