question_answer

The base of a triangular wall is 7 times its height. If the cost of painting the wall at Rs 350 per 100 square meter is Rs 1225, then what is the base length?

A) 50 m                            

B) 70 m

C) 75 m                            

D) 100 m

Correct Answer: B

Solution :

Let the height of the triangle be x. Then BC = 7x \[\Rightarrow \]Area of the \[\Delta \]ABC =         \[\frac{1}{2}\times 7x\times x\Rightarrow \frac{7}{2}{{x}^{2}}\] Cost of painting the wall at Rs 350 per 100sq. m. = Rs 1225 \[\therefore \] Cost of painting 100m2 = Rs 350 Cost of painting 1 m2 = Rs \[\frac{350}{100}\] \[\therefore \] Cost of painting \[\frac{7}{2}{{x}^{2}}=\frac{350}{100}\times \frac{7}{2}{{x}^{2}}\] \[\frac{350}{100}\times \frac{7}{2}\times {{x}^{2}}=1225\] (Given) \[\Rightarrow \,\,\,\,\,{{x}^{2}}=\frac{1225\times 100\times 2}{350\times 7}\Rightarrow {{x}^{2}}=100\] \[\Rightarrow \]    x = 10m \[\therefore \] Base = 7x = 70m