If an equilateral triangle of area X and a sq | vedclass

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

Question

(C) Let the side of the equilateral triangle be $a$ and the side of the square be $b$.The area of the triangle is $X = \frac{\sqrt{3}}{4} a^2$ and its

Vedclass · Accepted Answer

less than $Y$

Vedclass · Answer

(C) Let the side of the equilateral triangle be $a$ and the side of the square be $b$.The area of the triangle is $X = \frac{\sqrt{3}}{4} a^2$ and its perimeter is $P = 3a$.The area of the square is $Y = b^2$ and its perimeter is $P = 4b$.Since both have the same perimeter,$3a = 4b$,which implies $b = \frac{3a}{4}$.Now,$Y = b^2 = (\frac{3a}{4})^2 = \frac{9a^2}{16}$.From the area of the triangle,we have $a^2 = \frac{4X}{\sqrt{3}}$.Substituting this into the expression for $Y$,we get $Y = \frac{9}{16} 	imes \frac{4X}{\sqrt{3}} = \frac{9X}{4\sqrt{3}} = \frac{3\sqrt{3}X}{4}$.Since $\sqrt{3} \approx 1.732$,we have $Y \approx \frac{3 	imes 1.732}{4} X = 1.299X$.Therefore,$Y > X$,which means $X < Y$.

If an equilateral triangle of area $X$ and a square of area $Y$ have the same perimeter,then $X$ is

Similar Questions

In the given figure,$ABCD$ is a square of side $14 \ cm$. $E$ and $F$ are mid-points of sides $AB$ and $DC$ respectively. $EPF$ is a semicircle whose diameter is $EF$. $LMNO$ is a square. What is the area (in $cm^2$) of the shaded region?

How many metres of cloth $5\, m$ wide will be required to make a conical tent,the radius of whose base is $7\, m$ and height is $24\, m ?$ (in $m$)

$A$ circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular path is $132 \, m$. Its width is.....$m$.

Find the perimeter and area of the shaded portion of the adjoining diagram.

The ratio of the corresponding sides of two similar triangles is $3:4$. The ratio of their areas is

Vedclass Test Series

Exam Paper Generator

Online Exam Module