Question : If the numerical values of the height and the area of an equilateral triangle are the same, then the length of each side of the triangle is:
Option 1: 2 units
Option 2: 4 units
Option 3: 5 units
Option 4: 8 units
Correct Answer: 2 units
Solution : Let the side of an equilateral triangle be $a$ units. Let its height be $h$. Using Pythagoras theorem, we get, $a^2 = h^2+(\frac{a}2)^2$ ⇒ $h=\frac{\sqrt{3}}2a$ Area of equilateral triangle = $\frac{\sqrt{3}}{4}a^2$ sq. units According to the question, $\frac{\sqrt{3}}2a=\frac{\sqrt{3}}{4}a^2$ ⇒ $a=2$ units Hence, the correct answer is 2 units.
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