Question

An open rectangular tank is made of steel plate of area 1440cm it height is twice its width if the depth of the tank is 4 m less than width. Find its length

Answer 1

Let's assign variables to each dimension of the tank:
- Width = x
- Height = 2x
- Depth = x - 4

To find the length, we need to use the formula for the surface area of a rectangular tank:

Surface area = 2(length × width) + 2(length × height) + 2(width × height)

Since one of the sides is open, we won't consider that in the surface area formula. The surface area is given as 1440 cm².

1440 = 2(length × x) + 2(length × 2x) + 2(x × 2x)
1440 = 2x(length) + 4x(length) + 4x²
1440 = 6x(length) + 4x²

We also know that the area of a rectangle is given by length × width. In this case, the area is 1440 cm². Setting up the equation:

1440 = length × x

We can solve this equation for length by substituting length with 1440/x in the surface area equation:
1440 = 6x(1440/x) + 4x²
1440 = 8640/x + 4x²

To simplify, we can clear the fractions by multiplying both sides of the equation by x:
1440x = 8640 + 4x³

Rearranging the equation:
4x³ - 1440x + 8640 = 0

Factoring out a common factor of 4:
4(x³ - 360x + 2160) = 0

Dividing through by 4:
x³ - 360x + 2160 = 0

We can now use numerical or graphical methods to find the value of x that satisfies this equation. However, it is apparent that x = 12 is a solution.

So the width of the tank is 12 cm. The height is twice the width, so it is 2 * 12 = 24 cm. The depth is 4 m less than the width, so it is 12 - 4 = 8 cm.

Finally, we can find the length using the area equation:
1440 = length × 12
length = 1440 / 12 = 120 cm.

Therefore, the length of the tank is 120 cm.