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ICSE-VIII-Mathematics

20: Area of Trapezium and a Polygon Class 8 Maths

with Solutions - page 2
Qstn# A-10 Prvs-QstnNext-Qstn
  • #10
    The lengths of the sides of a triangle are in the ratio 4: 5: 3 and its perimeter is 96 cm. Find its area.
    Ans : Let the sides of the triangle ABC be 4x, 5x and 3x
    Let AB = 4x, AC = 5x and BC = 3x
    Perimeter = 4x + 5x + 3x = 96
    ⇒ 12x = 96
    ⇒ x = 96/12

    ∴ x = 8
    ∴ Sides are
    BC = 3(8) = 24 cm,
    AB = 4(8) = 32 cm,
    AC = 5(8) = 40 cm
    Since, (AC)2 = (AB)2 + (BC)2
    [∵ (5x)2 = (3x)2 + (4x)2]
    ∴ By Pythagoras Theorem , ∠B = 90˚
    ∴ Area of ΔABC = ½ (BC)(AB)
    = ½ (24)(32)
    = 12 × 32
    = 384 cm2