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.
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
1 answer
1 answer