The base of a right-angled triangle is \frac{4}{3} times the height of triangle. If the area of the triangle is 54 square cm, then what is the perimeter of the triangle?
- A. 30 cm
- B. 32 cm
- C. 36 cm ✓
- D. 40 cm
Correct Answer: C. 36 cm
Explanation
Let the height be 3x and base be 4x. Area = \frac{1}{2}(3x)(4x) = 6x^2 = 54 \implies x = 3. The sides are 9, 12, and hypotenuse \sqrt{9^2+12^2} = 15. Perimeter = 9 + 12 + 15 = 36 cm.
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