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

s = sqrt(2)s=2 miles

Explanation:

The dimensions of the rectangle are:

l = 2l=2
w = 1w=1

Now we use the area formula.

A = lw A=lw
A = (2)(1) A=(2)(1)
A = 2A=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 22.

Now we know that the formula for area for a square is A = s^2A=s2, so we could just plug in the area and solve for ss.

A = s^2A=s2
(2) = s^2(2)=s2
+-sqrt2 = sqrt(s^2)±2=s2
s=+-sqrt2s=±2

Your solution set would be:

s = -sqrt2s=2
s=sqrt2s=2

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=sqrt2s=2 miles