Posted by **Jordie ** on Wednesday, May 30, 2012 at 1:44pm.

For a given box, the height measures 4 meters. If the length of the rectangular base is 2 meters greater than the width of the base and the lateral area L is 96 square meters, find the dimensions of the box.

- Geometry -
**Reiny**, Wednesday, May 30, 2012 at 1:55pm
let the width be w

then length = x+2

SA = 2lw + 2lh + 2 wh

2w(w+2) + 2(w+2)(4) + 2(w)(4) = 96

2w^2 + 4w + 8w + 16 + 8w = 96

w^2 + 10w - 40 = 0

completing the square

w^2 + 10w + 25 = 40+25

(w+5)^2 = 65

w +5 = ±√65

w = -5 + √65 or x = -5 -√65 , the last being negative, thus resulting in "silly answer"

w = -5+√65 = appr. 3.06 or whatever number of decimals you want

so the width = 3.06

lenth = 5.06

height = 4

check:

2(3.06)(5.06) + 2(3.06)(4) + 2( 5.06)(4) = 95.92...

(not bad)

- Geometry -
**Steve**, Wednesday, May 30, 2012 at 2:01pm
area = 2(lh + wh)

you know that h=4, l=w+2, area=96

96 = 2((w+2)(4) + 4(4))

48 = 4w + 8 + 16

w = 6

the box is 6x8x4

- Geometry - PS -
**Steve**, Wednesday, May 30, 2012 at 2:06pm
hmm. forgot the w

96 = 2((w+2)(4) + w(4))

48 = 4w+8+4w

40 = 8w

w=5

box is 5x7x4

Lateral area is height*perimeter = 4*2(5+7) = 4*24 = 96

- Geometry -
**Reiny**, Wednesday, May 30, 2012 at 2:19pm
I think Steve has an error

2(5x7) + 2(5x4) + 2(7x4) ≠ 96

- Geometry -
**Steve**, Wednesday, May 30, 2012 at 3:41pm
Ahem. Lateral area does not include the bases.

- Geometry -
**Reiny**, Wednesday, May 30, 2012 at 11:31pm
Thanks Steve, didn't know that

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