Question

any idea how to solve this?

3. Bricks are delivered to a work site and stacked in rows and columns, forming a rectangular prism. The length of the prism is 1 foot greater than its width, and its height is 2 feet less than its width. Find the dimensions of the prism formed by the bricks, given that its volume is 40 cubic feet.

Answer 1

40=(length)x(width)x(height)

Answer 2

length = width+1
height = width-2

Answer 3

(w+1) (w) (w - 2) = 40

Answer 4

yes

Answer 5

solve for width

Answer 6

then you can find the other dimensions

Answer 7

(w^2+1) (W - 2) = 40
would i multiply them then go from there? :
W^3 - 2w^2 +1w -2 = 40

Answer 8

40 = (w+1)(w)(w-2)
= (w^2 +w)(w-2)
= (w^3 -2w^2 +w^2 -2w)
= (w^3 -w^2 -2w)

Answer 9

then go from there.

Answer 10

find the real solution of w

Answer 11

what happened to 40?
and would i use synt. div. to find w?

Answer 12

40 is still there

Answer 13

one sec

Answer 14

0 = w^3 - w^2 -2w -40

factor it:

0 = (w-4)(w^2 - 3w +10)

then you get your real solutions of w = 4 or you find the real solution of (w^2 - 3w +10) but since we already have w = 4. thats the answer

Answer 15

you can split 0 = (w-4)(w^2 - 3w +10) into 2 equations

0 = w-4 and 0 = (w^2 - 3w +10)

Answer 16

0 = w-4
4 = w


0 = w^2 - 3w + 10
-10 = w^2 -3w
-3.3 = w


is this correct?

Answer 17

well you dont need the second equation.
you already have 4. and there wouldnt be -dimensions in the question. so your width = 4

Answer 18

now you can find your length and height from the width

Answer 19

oh i see

so (4+1) x 4 x (4-2) = 40?

Answer 20

you tell me

Answer 21

it does thank you :) so i had to factor it after getting w+1 x w x w - 2 = 40 :)

Answer 22

i have to go lay down i cant stop coughing thank you again

Answer 23

no problem