Question

Think About the Process  The length of a rectangle is twice the width. The area of the rectangle is 92 square units. Notice that you can divide the rectangle into two squares with equal area. How can you estimate the side length of each​ square? Estimate the length and width of the rectangle.
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Part 1
How can you estimate the side length of each​ square?
A.
Estimate StartFraction StartRoot 92 EndRoot Over 4 EndFraction
.
B.
Estimate StartRoot 92 EndRoot.
C.
Estimate StartRoot 46 EndRoot.
Your answer is correct.D.
Estimate StartFraction StartRoot 46 EndRoot Over 4 EndFraction
.
Part 2
The rectangle is
  
enter your response here units long and
  
enter your response here units wide.
​(Round to the nearest tenth as​ needed.)

Answer 1

Part 1: C. Each square has area 92/2 = 46, so side length = sqrt(46).

Part 2: Let width = w. Then 2w·w = 92 ⇒ w^2 = 46 ⇒ w = sqrt(46) ≈ 6.8 units. Length = 2w ≈ 13.6 units.