What is the constant of proportionality in the relation of the area of an equilateral triangle to the square of length of its side?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{\sqrt{3}}{4}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{4}{\sqrt{3}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{\sqrt{4}}{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{\sqrt{3}}{4}$
Area of an equilateral triangle is $A = \frac{\sqrt{3}}{4} s^{2}$ where s is the length of one side the triangle.
Thus, Area ∝ square of the length of a side, with constant of proportionality $\frac{\sqrt{3}}{4}$ .

Suggest Corrections

Similar questions

Q. Area of an equilateral triangle is in proportion with square of its sides.

There is an equilateral triangle of side 5 cm. What is the length of the square whose area is equal to the area of the triangle ? (use construction)

Q. The area of an equilateral triangle describe on one side of a square is equal to half the area of the equilateral triangle describe on one of its diagonals

If all sides of a triangle are equal, it is called an equilateral triangle. In what all ways can we express the relation between the length of the side of an equilateral triangle and its perimeter?

Shorten them using letters.

Q. Prove that the area of an equilateral triangle described on the diagonal of a square is twice the area of an equilateral triangle described on its side.

Join BYJU'S Learning Program

What is the constant of proportionality in the relation of the area of an equilateral triangle to the square of length of its side?

The correct option is B √34Area of an equilateral triangle is A=√34s2 where s is the length of one side the triangle. Thus, Area ∝ square of the length of a side, with constant of proportionality √34.

The correct option is B $\frac{\sqrt{3}}{4}$
Area of an equilateral triangle is $A = \frac{\sqrt{3}}{4} s^{2}$ where s is the length of one side the triangle.
Thus, Area ∝ square of the length of a side, with constant of proportionality $\frac{\sqrt{3}}{4}$ .