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In The Figure above, the shaded rectangle is similar to the outer rectangle. The length of the outer rectangle is 4 feet and the perimeter of the outer rectangle is 14 feet. If the width of the shaded rectangle is 2 Feet, what is the area of the shaded rectangle?

In The Figure above, the shaded rectangle is similar to the outer rectangle. The length-example-1
User Gruuuvy
by
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1 Answer

7 votes

Answer:

5 1/3 square feet

Explanation:

You want the area of a rectangle whose width is 2 ft, if it is similar to one with a perimeter of 14 ft and a length of 4 ft.

Width

The perimeter can be used to find the width of the larger rectangle.

P = 2(L +W)

14 = 2(4 +W)

7 = 4 +W

3 = W

The width of the outer rectangle is 3 ft.

Scale factor

The width of the inner rectangle is 2 ft, so is 2/3 of the width of the outer rectangle.

The length of the shaded rectangle will be 2/3 of the length of the outer rectangle, so is ...

length = (2/3)(4 ft) = 8/3 ft

Area

The area of the shaded rectangle is ...

A = LW

A = (8/3 ft)(2 ft) = 16/3 ft² = 5 1/3 ft²

The shaded area is 5 1/3 square feet.

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Additional comment

You can also figure the area of the outer rectangle: (3 ft)(4 ft) = 12 ft². Then you can use the scale factor to find the shaded area:

shaded area = (12 ft²)(2/3)² = 48/9 ft² = 16/3 ft² = 5 1/3 ft²

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User Eric Wich
by
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