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.