question_answer

The cost of cutting grass from a triangular field at Rs. 45 per \[100\text{ }{{m}^{2}}\]is Rs. 900. Fine its height if twice the base of the triangle is 5 times the height.                        

A)  \[30\,m\]                     

B)  \[40\,m\]       

C)  \[50\,m\]                     

D)  \[10\,m\]      

Correct Answer: B

Solution :

(b): Area of Field: \[Rs\text{ }45\to 100\,{{m}^{2}}\] \[\therefore Rs900\to \frac{100}{45}\times 900=2000{{m}^{2}}\] \[A=\frac{1}{2}\left( 2b.\frac{h}{2} \right)=\frac{1}{2}.5h.\frac{h}{2}=\frac{5{{h}^{2}}}{4}\] Now \[\frac{5{{h}^{2}}}{4}=2000\Rightarrow {{h}^{2}}=1600\] \[=h=40\]