Question : The ratio of the sides of a triangle is 11 : 11 : 4. If the area of the triangle is $2\sqrt{117}$ cm, then what is the length of the equal sides?
Option 1: 3 cm
Option 2: 13 cm
Option 3: 11 cm
Option 4: 9 cm
Correct Answer: 11 cm
Solution :
Given: The ratio of the sides of a triangle is 11 : 11 : 4.
The area of the triangle is $2\sqrt{117}$ cm
2
.
A perpendicular bisector in an isosceles triangle bisects the base and acts as the height of the triangle.
Let the sides be $11x,11x,$ and $4x$
Then, the height AD = $\sqrt{(11x)^2-(2x)^2}=\sqrt{117x^2}$
Area of a triangle = $\frac{1}{2}$ × Base × Height
⇒ $\frac{1}{2}×4x×\sqrt{117x^2}=2\sqrt{117}$
⇒ $x^2=1$
⇒ $x=1$
So, the length of the equal sides = (11 × 1) = 11 cm
Hence, the correct answer is 11 cm.
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