• # question_answer 9) Base and height of a right angled triangle are in the ratio of 5 : 7 and area is $\mathbf{70}\text{ }\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}$. Find the base and height of the triangle. A) 12 cm and 14 cmB)        10 cm and 14 cmC) 7 cm and 14 cm  D)        9 cm and 14 cmE) None of these

Explanation Option [b] is correct. Lets consider the common multiplier x. According to the question $70=\frac{1}{2}\times 5x\times 7x\Rightarrow 70=\frac{35{{x}^{2}}}{2}$ $\Rightarrow 140=35{{x}^{2}}\Rightarrow {{x}^{2}}=\frac{140}{35}=4$ $\Rightarrow x=\sqrt{4}=2cm$ Hence, base of the triangle $=5\times 2=10cm$ and height $7\times 2=14cm.$