Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

The height of a box is 7 inches. Its length is 6 inches more than its width. Find the length if the volume is 280
cubic inches.

Sagot :

iGreen
h = 7
l = w + 6
V = 280

V = lwh

Plug in what we know:

280 = (w + 6)(w)(7)

Distribute W into the first parenthesis:

280 = (w^2 + 6w)(7)

Distribute 7:

280 = 7w^2 + 42w


Divide 7 to both sides:

40 = w^2 + 6w

Subtract 40 to both sides:

w^2 + 6w - 40 = 0

Factor:

(w - 4)(w + 10) = 0

Therefore, w = 4.

Plug this back into the equation for the length:

l = w + 6

l = 4 + 6

l = 10
dln
[tex]Volume=Length*Width*Height \\ 280=(x+6)*x*7 \\ 280=7x(x+6) \\ 280=7x^{2}+42x \\ 0=7x^{2}+42x-280 \\ 0=7(x^{2}+6x-40) \\ 0=7(x+10)(x-4) \\ Since\ we\ can't\ have\ negative\ values,\ x=4 \\ Width=4 \\ Length=Width+6 \\ Length=4+6 \\ \boxed{Length=10}[/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.