Question

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.

• A. 2
• B. \(\sqrt2\)
• C. 3
• D. \(\sqrt3\)

Answer 1

The Correct Option is D

The area of a given triangle is presented as \(9y\) cm². To find \(y\), we have to equate this to the area of an equilateral triangle with a side length of 6 cm. The formula for the area of an equilateral triangle with side \(a\) is \(\frac{\sqrt{3}}{4}a^2\). So, substitute \(a=6\):

\(\text{Area}=\frac{\sqrt{3}}{4}\times6^2=\frac{\sqrt{3}}{4}\times36=9\sqrt{3}\)

Now, set the areas equal to solve for \(y\):

\(9y=9\sqrt{3}\)

To find \(y\), divide both sides by 9:

\(y=\sqrt{3}\)

Thus, the value of \(y\) is \(\sqrt{3}\).