Question

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 width. What is the width in inches of the gift box?

Answer 1

Step-by-step explanation:

Volume of gift box=450^3 inches

Let length, breadth and height of box be l,b and h

According to question

b=l-4

so,l=b+4 (1)

h=2b (2)

Now volume of Box=450

lbh=450

(b+4)b(2b)=450

2b^3+8b^2=450

2(b^3+4b^2)=450

b^3+4b^2=225

b^3+4b^2-225=0

(b-5)(b^2+9b+45)=0

b^2+9b+45 can't be factorised as its discriminant is lesser than 0:

Discriminant,D=b^2-4ac

=(9)^2-4(1)(45)

=81-180

=-99

Therefore width of box,b=5 inches

Hope it helps you