The total surface area of a triangular based prism is \[576c{{m}^{2}}\] and its height is 22cm. IF the area of its base is \[24c{{m}^{2}}\], find the perimeter of its base.

Hint: For solving this question you should know about the total surface area and the perimeter of a triangular based prism. In this problem first we will find the total surface area in terms of perimeter of base, and then by using the given data we will find the values of its perimeter in terms of cm.


Complete step-by-step solution:
According to the question the total surface area of a triangular based prism is given as \[576c{{m}^{2}}\] and the height of this is given 22cm. And if the area of its base is \[24c{{m}^{2}}\], then it is asked to find the perimeter of its base.
The general formula for the total surface area of a right prism is Total surface area (TSA) \[=Ph+2B\] where P presents the perimeter of the base, h is the height of the prism and B is the area of the base.
Since, the total surface area TSA \[=576c{{m}^{2}}\] and the base is \[B=24cm\] and the height is \[h=22cm\], therefore, the perimeter of its base is:
\[\begin{align}
  & TSA=Ph+2B \\
 & \Rightarrow 576=22P+\left( 2\times 24 \right) \\
 & \Rightarrow 576=22P+48 \\
 & \Rightarrow 22P=576-48 \\
 & \Rightarrow 22P=528 \\
\end{align}\]
So, the value of P will be
\[\Rightarrow P=\dfrac{528}{22}=24\]
Hence, the perimeter of its base is 24cm.

Note:While solving this type of questions you should be careful of all the measures of the dimensions and use the correct parameter in the formula as it is given in the question. Because if any single one digit will be wrong then the whole question will be wrong. So, solve this carefully.