Chapter MPS, Problem 9.2MPS

To determine

To find: The perimeter of the given figure.

Answer to Problem 9.2MPS

  $\left(\frac{3x^2+222}{x}\right)cm$

Explanation of Solution

Given:

The area of rectangle $=111sq.cm$

Triangle is equilateral

  

Formula Used:

Sum of all side of given figure = $AB+BC+CD+DE+AE$

Calculation:

  

Let length of rectangle be $l$ and breadth be $x$

Since the $△$ is equilateral

So, AB=AE= $x$

Now, the area of rectangle =111 $c{m}^2$

  $\begin{array}{l}\Rightarrow length\times breadth=111\\ \Rightarrow l\times x=111\\ \Rightarrow l=\frac{111}{x}\end{array}$

Perimeter of given figure = sum of all side of figure

  $\begin{array}{l}=AB+BC+CD+DE+AE\\ =x+l+x+l+x\\ =x+x+x+l+l\\ =3x+2l\\ =3x+2\times \frac{111}{x}\\ =\left(\frac{3x^2+222}{x}\right)cm\end{array}$

Conclusion:

Thus the required perimeter is $\left(\frac{3x^2+222}{x}\right)cm$ .