question_answer

A plot of ground is in the form of an isosceles triangle. The cost of the triangular land is Rs. 50,000 at the rate of Rs. 125per square metre  If the length of the base is 40m, then the length of equal sides is

A) \[20\sqrt{3}\,m\]m           

B)         \[22\sqrt{3}\,m\]

C) \[22\sqrt{2}\,m\]           

D)        \[20\sqrt{2}\,m\]  

Correct Answer: D

Solution :

 If height of the triangle is h, then its area \[=\frac{1}{2}\times 40\times h\] \[=2c{{m}^{2}}h0\] Cost of this triangular land \[=Rs.\,125\times 20\,h\] \[\therefore \]  \[125\times 20h=50,000\]                 or            \[h=20\,cm\]                 \[AB=\sqrt{A{{D}^{2}}+B{{D}^{2}}}\]                 \[=\sqrt{{{h}^{2}}+{{20}^{2}}}\]                 \[=20\sqrt{2}\,cm\]