• # question_answer Let$\Delta \text{ABC}$be a triangle whose vertices are (0, 0), (a, 5) and (-5, 5) respectively. If the triangle is right-angled at A, find the value of 'a'. A)  3                             B)         5 C)  2                             D)         6

Let A(0,0), B(a,5)and C(-5,5) be the vertices of the triangle. Therefore, $\Delta \text{APB }\tilde{\ }\text{ }\Delta \text{DPC}$ $\Rightarrow$ $\frac{AP}{DP}=\frac{PB}{PC}=\frac{AB}{DC}$ $\Rightarrow$ $AP\times PC=PB\times DP$ $\frac{1}{2}\sqrt{{{b}^{2}}+{{c}^{2}}}\times AD=\frac{1}{2}bc$ $\Rightarrow$$AD=\frac{bc}{\sqrt{{{b}^{2}}+{{c}^{2}}}}$