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katrin2010 [14]
3 years ago
8

A gift box has a volume of 450 cubic inches. The width of the box is 4 inches less than the length. The height is twice the widt

h. What is the width in inches of the gift box?
Mathematics
1 answer:
VashaNatasha [74]3 years ago
5 0

Answer:

width = 5 in

length = 5+4=9 in

height = 2(5)= 10 in

Step-by-step explanation:

A gift box has a volume of 450 cubic inches.

Let 'w' be the width of the box

The width of the box is 4 inches less than the length.

length = w+4

The height is twice the width.

height = 2 \cdot width

height = 2w

Volume of box = length times width times height

V=(w+4)(w)(2w)

450=(w+4)(w)(2w)

450=2w^3+8w^2

2w^3+8w^2-450=0

\quad 2\left(w-5\right)\left(w^2+9w+45\right)=0

w-5=0

w=5

\quad\left(w^2+9w+45\right)=0, this gives two complex values

so width = 5

length = 5+4=9

height = 2(5)= 10

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