Question

The top of a cuboid box has an area of 720 square inches, the side has 800 square inches and the front has 360 square inches. So, what are the height, width and length or depth?​

Answer 1

Answer:

Height= 20, Width=40, Length= 18

Step-by-step explanation:

Let a be the length, b be the height and c be the width of the cuboid.

It is given that the area of the top portion is 720. So we are taking the top to include length and width. So 720= a*c.

It is given that the area of the side portion is 800. So we are taking the side to include height and width. So 800= b*c.

It is given that the area of the front portion is 360. So we are taking the front to include length and height. So 360= a*b.

Now let's divide 720 by 800. we get :

720/800= (a*c)/(b*c)=a/b=9/10

or a= b*(9/10).

Subsitute this in : 360=a*b.

We get : 360= b*(9/10)*b

360=b*b*(9/10)

or

3600/9=b*b

or

400=b*b

or

b=20

Now from the last relation we get:

360=a*b=a*20

or

360/20=a

or

a=18

Now the first relation we get:

720=a*c=18*c

or

c=720/18

or

c=40

Therefore :

length= a =18

height = b= 20

width= c = 40