Question

Think About the Process The length of a rectangle is twice the width. The area of the rectangle is 9

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.

Answer 1

The side length of each square is 2.12 units.

The length ad width of the rectangle are 2.12 and 4.24 units

Explanation:

Let the width of the rectangle is x,

So, the length of the rectangle is 2x.

Area of the rectangle = 9 sq. units

`9 = 2x * x` [as area = length x width]

`\Rightarrow 9 = 2x^2`

`\Rightarrow x^2 = (9)/(2)=4.5`

`\Rightarrow x = 1.5√(2)=2.12` units

So, width of the rectangle, x= 2.12 units and

the llengthof the rectangle, 2x= 2 x 2.12= 4.24 units.

After division of the rectangle into two equal square, so, the area of each square will be half of the area of the rectangle.

The area of the rectangle = 9/2=4.5 square units.

Let a be the length of the sides of the square, so

Area
`= a^2`

`\Rightarrow a^2=4.5`

`\Rightarrow`
`a = 1.5√(2)=2.121`

Hence, the side length of each square = 2.12 units.