Question

Think About the Process  The length of a rectangle is twice the width. The area of the rectangle is 74 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 StartRoot 37 EndRoot.
Your answer is correct.B.
Estimate StartFraction StartRoot 37 EndRoot Over 4 EndFraction
.
C.
Estimate StartFraction StartRoot 74 EndRoot Over 4 EndFraction
.
D.
Estimate StartRoot 74 EndRoot.
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: A. sqrt(37).

Reason: Let width = w and length = 2w. Area = 2w^2 = 74 ⇒ w^2 = 37 ⇒ w = sqrt(37).

Part 2: width = sqrt(37) ≈ 6.1 units, length = 2·sqrt(37) ≈ 12.2 units.