Construct Square with Same Area as a Given Rectangle - UGA
Construct Square with Same Area as a Given Rectangle
Problem: Given a rectangle with side lengths of a and b, construct a square with the same area. Solution: Given is the rectangle with i) sides and , ii) Area = . We want to construct a square with same area. First, let's construct the segment . Then construct a circle with center at point and radius . Then extend the segment and it intersect the circle at point . Now is the midpoint of segment .
Now, construct a circle with center at point and radius . If we extend the segment it intersect the circle at points and .
Next, construct a square with be the one side. So we have a Square .
Claim: Area of Rectangle
is same as the area of Square .
By construction, is the geometric mean of sides and . So, .
So, area of Rectangle
is same as the area of the Square .
. Hence area of Square
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