Question

The volume of a rectangular box is given by the formula v=LWH. The volume of the box is 495Cu. units. find the width and length. ( L=x+2, width=x, ht=5

Answer 1

Okay, let's put this into the form of an equation. Since l*w*h = 495, we can say:\[495=(x+2)(x)(5).\]
By that,
\[495=(5x ^{2}+10x)\]
Now, just solve for x. Let's divide by 5 on both sides to eliminate the coefficient on the x^2.
495/5=99.
\[99=x ^{2}+2x\]
From here we factor to solve for x. Let's put it in the form of a quadratic, so:
\[x ^{2}+2x-99=0.\]
Do you know how to factor?

Answer 2

Not strong for this type

Answer 3

Okay, so we'll factor this like any other quadratics. Quadratics are typically in this form:\[ax ^{2}+bx+c=0.\]
That being said, one common method to factor a quadratic is to factor the value of the third term into two values that will equal the coefficient of the b term if they're added together. Can you solve this, Dede?

Answer 4

I'll try

Answer 5

Can u walk me through this?

Answer 6

Sure. We need to factor 99 and find two factors that add to equal 2. Now tell me, what two factors add to equal 2?

Answer 7

1s

Answer 8

11 and 9

Answer 9

Oops, what factors would equal -99?

Answer 10

-9 and 11

Answer 11

Yup! From here, we can put these in the from of two sets of parentheses, like this:
\[(x-9)(x+11)\]and set that equal to zero. Then, you solve each separate set of parentheses like such:
\[(x-9)=0 ...x=9\]
\[(x+11)=0...x=-11\]
Now, we can only take one value of x, the positive value, do you understand why?

Answer 12

Yes cos it can't be a negative #

Answer 13

Yep. So then you plug it into the original question and solve for the length and width:
\[l=x+2...l=(9)+2\]
\[w=x\]

Answer 14

width(x) equal to 9 and length x+2 =11

Answer 15

Yep! Congratulations! Hope this helped. :)