## Dede 3 years ago 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

1. Schrodinger

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?

2. Dede

Not strong for this type

3. Schrodinger

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?

4. Dede

I'll try

5. Dede

Can u walk me through this?

6. Schrodinger

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?

7. Dede

1s

8. Dede

11 and 9

9. Schrodinger

Oops, what factors would equal -99?

10. Dede

-9 and 11

11. Schrodinger

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?

12. Dede

Yes cos it can't be a negative #

13. Schrodinger

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

14. Dede

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

15. Schrodinger

Yep! Congratulations! Hope this helped. :)