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    Question

    In a right triangle ABC, angle B = 90°. If tan A = 3/4

    and the length of the hypotenuse is 25 cm, find the area of the triangle.
    A 150 cm² Correct Answer Incorrect Answer
    B 175 cm² Correct Answer Incorrect Answer
    C 159 cm² Correct Answer Incorrect Answer
    D 100 cm² Correct Answer Incorrect Answer

    Solution

    ATQ,

    We have a right triangle with: tan A= 3/4, meaning the opposite side is 3x and the adjacent side is 4x. The hypotenuse is 25 cm.

    Use the Pythagorean theorem: (3x)2 + (4x)2 = 252

    Solve for x, which gives x=5. The sides of the triangle are: Opposite side = 3x=15 cm, Adjacent side = 4x=20 cm. The area is = (1/2) × 15 cm × 20 cm = 150 cm2

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