An equilateral triangle,a square,and a circle | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the perimeter be $P$. Since the perimeters are equal,we have $3a = 4b = 2\pi r = P$,where $a$ is the side of the triangle,$b$ is the side of t

Vedclass · Accepted Answer

$T < S < C$

Vedclass · Answer

(C) Let the perimeter be $P$. Since the perimeters are equal,we have $3a = 4b = 2\pi r = P$,where $a$ is the side of the triangle,$b$ is the side of the square,and $r$ is the radius of the circle.$1$. Area of the equilateral triangle: $T = \frac{\sqrt{3}}{4} a^2 = \frac{\sqrt{3}}{4} \left(\frac{P}{3}\right)^2 = \frac{\sqrt{3}}{36} P^2 \approx 0.0481 P^2$.$2$. Area of the square: $S = b^2 = \left(\frac{P}{4}\right)^2 = \frac{1}{16} P^2 = 0.0625 P^2$.$3$. Area of the circle: $C = \pi r^2 = \pi \left(\frac{P}{2\pi}\right)^2 = \frac{P^2}{4\pi} \approx 0.0796 P^2$.Comparing the coefficients of $P^2$: $0.0481 Thus,$T < S < C$.

An equilateral triangle,a square,and a circle have equal perimeters. If $T$ denotes the area of the triangle,$S$ the area of the square,and $C$ the area of the circle,then

Similar Questions

The radius of the wheel of a vehicle is $70\, cm$. The wheel makes $10$ revolutions in $5\, seconds$. The speed of the vehicle is......$km/h$.

If a diagonal of a square is doubled,how does the area of the square change?

The perimeter of a right-angled triangle is $90\, cm$ and its hypotenuse is $39\, cm$. Find its other sides.

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes.

Vedclass Test Series

Exam Paper Generator

Online Exam Module