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A small painting has an area of 400 cm^2. The length is 4 more than two times the width. Find the dimensions of the painting. Solve by completing the square. Round answers to the nearest tenth of a centimeter.
Help.
+9479 width = w
length = 2w + 4
area = length * width
400 = (2w + 4) * (w)
Distribute.
400 = 2w2 + 4w
Divide through by 2.
200 = w2 + 2w
Add (2/2)2 , or 1, to both sides.
200 + 1 = w2 + 2w + 1
Now the right side is a perfect trinomial and can be factored.
201 = (w + 1)(w + 1)
201 = (w + 1)2
Take the square root of both sides.
±√(201) = w + 1
w = -1 ± √(201)
Exclude the negative option since we are talking about distance.
w ≈ 13.2 cm
l ≈ 2(13.2) + 4 ≈ 30.4 cm
