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
Nov 23, 2017
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
Now we know that the formula for area for a square is
#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