6th Class Mental Ability Geometry Question Bank Geometry

  • question_answer 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 cm

    B)        10 cm and 14 cm

    C) 7 cm and 14 cm  

    D)        9 cm and 14 cm

    E) None of these

    Correct Answer: B

    Solution :

    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 \[7\times 2=14cm.\]


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