Question

A large chocolate bar has been base of the area of 42.30 square feet in the length is 0.4 foot shorter than twice its width. find the length and the width of the bar

Answer 1

4.7 ft= width

9 ft = length

Explanation:

Let w = width

2w - .4 = length

A = lw

42.30 = w(2w - .4)

`42.3 = 2w^(2) - .4w`

`2w^(2) -.4w - 42.3 = 0`

let's remove the decimals by multiplying thru by 10

`20w^(2) - 4w - 423 = 0`

(2w + 9)(10w - 47) = 0

2w + 9 = 0 or 10w - 47 = 0

2w = -9 or 10w = 47

w = -9/2 = -4.5 or w = 47/10 = 4.7

Length cannot be negative, so -4.5 must be ignored

Therefore, w = 4.7 ft= width

2w - .4 = 2(4.7 -.4) = 9.4 - .4 = 9 ft = length

Answer 2

Length is 9 feet, width = 4.7 feet.

Explanation:

Let L = length and W = the width. Then:

L = 2W - 0.4 also:

LW = 42.3

So L = 42.3/W

Plug this into the first equation:

42.3/W = 2W - 0.4 Multiply thru by W:

42.3 = 2W^2 - 0.4W

2W^2 - 0.4W - 42.3 = 0

W = [0.4 +/- sqrt((-0.4)^2 - 4*2* -42.)) ] / 2*2

W = 4.7.

So L = 42.3 / 4.7

L = 9.