Question

The total surface area of a tank is 1600m2.The length, breadth, height in ratio is fallows as 2:2:1.Find the tank's diagonal.​

Answer 1

Let the common ratio be x

Therefore:

2x:2x:x

As the length and the breadth are same and the height is different,it tells us that the polyhedron is a cuboid.

Total surface area of a cuboid =2 (lb)+2 (bh)+2 (hl)

Putting the values in the formula:

2(2x×2x)+2 (2x×x) +2(2x×x)

2 (4x^2)+2 (2x^2)+2(2x^2)

8x^2+4x^2+4x^2

16x^2

Total surface area of cuboid=1600 sq m

16x^2=1600

x^2=1600/16

x^2=100

x=10 m.

Using hypotenuse theorem where the hypotenuse side is the diagonal.

h^2=b^2+p^2

h^2=10^2+10^2

h^2=100+100

h^2=200

h=10 root 2

Therefore the length of the diagonal is 10 root 2 m.