Question
In a triangle, the lengths of the sides are proportional
to 4, 3, and 5. If the area of this triangle is 216 square centimeters, determine the triangle's perimeter.Solution
Since, the sides of the triangle are in ratio 3:4:5, the given triangle is a right-angled triangle. Let the three sides of the triangle be '3x' cm, '4x' cm and '5x' cm, respectively So, area of the triangle = (1/2) X (3x) X 4x = 216 Or, 6x2 = 216 Or, x2 = 36 So, x = ±6 Since, length of side cannot be negative, x = 6 So, required perimeter = 6 X (3 + 4 + 5) = 72 cm Hence, option a.
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