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    Question

    If the area of a triangle is 1690 cm2 and

    base: corresponding altitude is 4:5, then the altitude of the triangle is:
    A 33 cm Correct Answer Incorrect Answer
    B 75 cm Correct Answer Incorrect Answer
    C 60 cm Correct Answer Incorrect Answer
    D 65 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 4x and 5x respectively. According to question, ⇒ 1/2 x base × altitude = 1690 cm2 or, ⇒ 1/2 x (4x) x (5x) = 1690 ⇒ 20x2 = 3380 ⇒ x2 = 3380/20 ⇒ x2 = 169 ⇒ x = √169 ⇒ x = 13 cm Altitude of a triangle = 5x = 5 × 13 cm = 65 cm

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