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

#1**+4 **

width = w

length = 2w + 4

area = length * width

400 = (2w + 4) * (w)

Distribute.

400 = 2w^{2} + 4w

Divide through by 2.

200 = w^{2} + 2w

Add (2/2)^{2} , or 1, to both sides.

200 + 1 = w^{2} + 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