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# Complete the square question

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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.

gobromash  Apr 10, 2017
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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

hectictar  Apr 10, 2017

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