The ratio of the sides of a triangle is 11 : 11 : 4. If the area is 2$\sqrt{117}$ cm², then what is the length of the equal sides?
Answer & explanation
Correct answer: option 3
Area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$
where, s = semi-perimeter
a, b, c is the sides
Let the sides of the triangle = $11x, 11x, 14x$
s = $\frac{11x+11x+4x}{2}$
= 13x
Area = $\sqrt{13x(13x-11x)(13x-11x)(13x-4x)}$
= $\sqrt{13x \times 2x \times 2x \times 9x}$
= 2x²$\sqrt{117}$
Given that area = 2$\sqrt{117}$ cm²
x = 1,
Thus, the sides of the triangle = 11cm, 11cm, 4cm