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Dede
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
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?
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?
Can u walk me through this?
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?
Oops, what factors would equal -99?
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?
Yes cos it can't be a negative #
Yep. So then you plug it into the original question and solve for the length and width: \[l=x+2...l=(9)+2\] \[w=x\]
width(x) equal to 9 and length x+2 =11
Yep! Congratulations! Hope this helped. :)