The sides of a triangle are in the ratio 3 : 4 : 5. If the perimeter of this triangle is 36 cm, what is its total surface area?
(a) 54 cm²
(b) 60 cm²
(c) 72 cm²
(d) 108 cm²

Answer: A. 54

• Answer: (a) 54 cm²
• Solution:
1. Let the actual side lengths of the triangle be 3x, 4x, and 5x.
2. Use the given perimeter to find the scale factor x:
\(3x+4x+5x=36\implies 12x=36\implies x=3\)
3. Calculate the true lengths of the sides:
\(\text{Side\ 1}=3(3)=9\text{\ cm},\quad \text{Side\ 2}=4(3)=12\text{\ cm},\quad \text{Side\ 3}=5(3)=15\text{\ cm}\)
4. Notice that 9² + 12² = 81 + 144 = 225 = 15². This satisfies the Pythagorean theorem, proving it is a right-angled triangle.

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