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 = 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
Now we know that the formula for area for a square is
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