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    Question

    If the area of a triangle is 1014 cm2 and

    base: corresponding altitude is 3:4, then the altitude of the triangle is:
    A 70 cm Correct Answer Incorrect Answer
    B 48 cm Correct Answer Incorrect Answer
    C 80 cm Correct Answer Incorrect Answer
    D 52 cm Correct Answer Incorrect Answer

    Solution

    Using the formula, Area of the triangle = 1/2 x base x height   Let the base and altitude be 3x and 4x respectively. According to question, ⇒ 1/2 x base × altitude = 1014 cm2 or, ⇒ 1/2 x (3x) x (4x) = 1014 ⇒ 12x2 = 2028 ⇒ x2 = 2028/12 ⇒ x2 = 169 ⇒ x = √169 ⇒ x = 13 cm Altitude of a triangle = 4x = 4 × 13 cm = 52 cm

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