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    Subject

    Quantitative Aptitude

    Topic

    Areas & Volumes

    The altitude drawn to the base of an isosceles triangle is 8cm and the perimeter is 32cm. Find the area of the triangle?

    ক)
    50
    খ)
    60
    গ)
    70
    ঘ)
    80

    Explanation

    let ABC be the isosceles triangle, the AD be the altitude Let AB = AC = x then BC= 32-2x       [because parameter = 2 (side) + Base] since in an isoceles triange the altitude bisects the base so BD = DC = 16-x In a triangle ADC = (AC)2=(AD)2+(DC)2\left(AC\right)^2=\left(AD\right)^2+\left(DC\right)^2 x2=82+(16−x)2x^2=8^2+\left(16-x\right)^2 ⇒x=10\Rightarrow x=10 BC = 32-2x = 32-20 = 12 cm Hence, required area = 12∗BC∗AD\frac12\ast BC\ast AD = 12∗12∗10\frac12\ast12\ast10 = 60 sq cm

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