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    ​The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then what is the measure of AB?​
    Question

    The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then what is the measure of AB?

    A.

    203\frac{20}{3} cm

    B.

    2003\frac{200}{3} cm

    C.

    1063\frac{10\sqrt{\smash[b]{6}}}{3} cm​

    D.

    15 cm

    Correct option is D

    Given:

    ∆ABC ~ ∆PQR (Similar triangles)

    Perimeter of ∆ABC = 36 cm

    Perimeter of ∆PQR = 24 cm

    PQ = 10 cm

    Concept Used:

    The ratio of perimeters of two similar triangles is equal to the ratio of their corresponding sides.

    Solution:

    ABPQ=Perimeter of △ABCPerimeter of △PQR=32\frac{AB}{PQ} = \frac{Perimeter of △ABC​ }{Perimeter of △PQR} = \frac{3}{2}​  

    Substitute PQ = 10cm 

    AB10=32\frac{AB}{10}=\frac{3}{2} 

    AB = 10×32=1510 \times \frac{3}{2} = 15cm

    AB = 15cm

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