Question : The area of a triangle is 96 cm2 and the ratio of its sides is 6 : 8 : 10. What is the perimeter of the triangle?
Option 1: 48 cm
Option 2: 56 cm
Option 3: 64 cm
Option 4: 44 cm
Correct Answer: 48 cm
Solution :
Given: The ratio of the length of sides is 6 : 8: 10 and the area of the triangle is 96 cm
2
.
Let the sides be $6x$ cm, $8x$ and $10x$ cm.
By heron's formula, Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
where, $s=\frac{a+b+c}{2}$
Here, $s=\frac{6x+8x+10x}{2}=12x$
So, $\sqrt{12x(12x-6x)(12x-8x)(12x-10x)}$ = $96$
⇒ $\sqrt{12x(6x)(4x)(2x)}$ = $96$
⇒ $24x^2$ = $96$
⇒ $x^2 = 4$
⇒ $x=2$
Now, the Perimeter of the triangle
= $2s$ = $24x$ = 48 cm
Hence, the correct answer is 48 cm.
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