# What is the length of lace to be put around a curtain which has an area of 32 sq feet and the length is 4 times the width.

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### 3 Answers

length = 4w and widt = w by data.

Area 32 sq ft = 4w*w

w^2 = 32/4 = 8

w = sqrt8 = 2sqrt2.

Perimeter = 2(length+width) = 2(4w+w) = 10w = 10(2*sqrt2) = 20sqrt2 = 28.2843 ft and that is the length of the lace.

Area of a rectangle's equation is l x w = a. You know that the area is 32 sq feet and that the length is 4 times the w or 4 x w. So you can set up an equation (4W)(W) = 32. The W are multiplied together and you get W^2. Your equation now is 4W^2 = 32. Divide both sides by 4 and you get W^2 = 8. Take the square root of both sides and you are left with W = 2 sq rt 2. That is the width. Then you need to plug that into the length's equation. 4 x W = 4 x 2 sq rt 2 = 8 sq rt 2.

The length of ribbion is the perimeter and so you now need to add all sides. 2 sq rt 2 + 2 sq rt 2 + 8 sq rt 2 + 8 sq rt 2 = 20 sq rt 2!

Let’s assume the width of the curtain is W. As the length is 4 times the width , length = 4W. Now the area of the curtain is given by length * width = W * 4W = 4W^2

The area is 32.

=> 4W^2 = 32

=> W^2 = 8

=> W = 2 sqrt2

So the length is 8 sqrt 2.

Now the perimeter is 2W + 2L = 2W + 8W = 10 W = 20 sqrt 2

So the lace required for the curtain is 20 sqrt 2 feet.