A box with no top is to be constructed from a piece of...

A box with no top is to be constructed from a piece of cardboard whose length measures 6 inches more than its width. The box is formed by cutting squares that measure 2 inches on each side from the four corners and then folding up the sides. If the volume of the box will be 14 in^3, what are the dimensions of the piece of cardboard?

Transcript

00:03 All right, we're given a piece of cardboard, and we're going to cut two inches out of each corner, all right, as shown in the diagram here.

00:12 And then basically what we're going to do is fold it up into an open -topped box.

00:17 All right, so we'd fold along those dotted lines there, fold that side up.

00:22 And what's going to happen is we'll end up with a box, right? that's going to look something like this, where we know that.

00:32 That, okay, so it looks more or less like that.

00:36 We know that it's going to be two units tall, right? because that's how tall each of these flaps are that we cut out.

00:43 So it's going to be two units tall.

00:44 This side was originally w, but i cut out two twice.

00:50 So this side would be w minus four.

00:53 All right, so whatever the original width was, i've taken off four inches two from each side.

00:57 This one was originally l, but they told us that this length was the width.

01:02 6 more than the width, so i'm just going to use w plus 6.

01:06 But again, i have to subtract 2 from that side, 2 from that side, so w plus 6, but then minus 4.

01:14 So that's going to be w plus 2.

01:17 So w plus 2 would be this length overall.

01:20 So that's what the dimensions of our box look like once we've cut out the 2 inches on the corners and folded it up.

01:27 All right.

01:28 Now, we're told that the volume is equal to 14 cubic.

01:32 So i know that the volume is equal to 2 times w minus 4 times w plus 2.

01:41 All right.

01:41 So length times width times height.

01:43 I did height times length times with, whatever means the same thing.

01:46 So now let's go ahead and try and solve this.

01:49 I'm going to divide each side by 2 and i'll get 7 is equal to.

01:52 And i'm also going to distribute that would be w squared.

01:56 It's going to be plus 2w and then minus 4w and then minus 4w and then minus 7.

02:02 Make sure you're careful when you distribute, when you multiply these two binomials together to get those middle terms.

02:09 All right.

02:10 I'm going to subtract the 7 from both sides, so i'm going to be left with w squared, and i'm going to combine these two middle terms here.

02:17 I have 2w minus 4w, that's minus 2w.

02:21 And remember, i subtracted 7...

Question

Please give Ace some feedback