The area of a triangle is 9y cm2. Find the value of y if its area is equal to the area of an equilateral triangle having side 6 cm.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\sqrt{3}\)
The area of an equilateral triangle of side \(a\) is \(\displaystyle\frac{\sqrt{3}}{4}a^2\). The given area 9y is equal to this area.
Area of the equilateral triangle: \(\displaystyle\frac{\sqrt{3}}{4}\times6^2=9\sqrt{3}\) cm2
The given area equals this area: \(9y=9\sqrt{3}\), so \(y=\sqrt{3}\)