Question

plzz help me...... ​

Answer 1

$\underline{\underline{\sf{ \color{magenta}{\qquad Given\:: \qquad} }}}$

A circle and equilateral triangle whose diameter and side are equal

$\underline{\underline{\sf{ \color{magenta}{\qquad To\:Find\:: \qquad} }}}$

Ratio of their areas:—

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Let diameter of circle = 2x

∴ Side of triangle also = 2x

So , Radius of circle = 2x/2 = x

$\underline{\underline{\sf{ \color{magenta}{\qquad Diagrams\:: \qquad} }}}$

$\bold\red{(1)\:Circle}$

Radius of circle = x

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large x}\end{picture}$

$\bold\red{(2)\:Triangle}$

Side of triangle = 2x

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

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$\underline{\underline{\sf{ \color{magenta}{\qquad Solution\:: \qquad} }}}$

❛❛Ratio of their areas❜❜ :-

$\longmapsto\:\tt{\bigg(\dfrac{(Area\:of\:circle)}{(Area\:of\:equilateral\:triangle)}}\bigg)$

$\longmapsto\:\tt{\bigg(\dfrac{\pi r^2}{\frac{\sqrt{3}}{4}(side)^2}}\bigg)$

$\longmapsto\:\tt{\bigg(\dfrac{(\pi)\:\times\:(x)^2}{\frac{\sqrt{3}}{4}\:\times\:(2x)^2}}\bigg)$

$\longmapsto\:\tt{\bigg(\dfrac{\pi \:\times\:x^2}{\frac{\sqrt{3}}{4}\:\times\:2x\:\times\:2x}}\bigg)$

$\longmapsto\:\tt{\bigg(\dfrac{\pi\:\times\: x^2}{\frac{\sqrt{3}}{4}\:\times\:4x^2}}\bigg)$

$\longmapsto\:\tt{\bigg(\dfrac{\pi \:\times\:x^2}{\frac{\sqrt{3}}{\cancel{4}}\:\times\:\cancel{4}\:\times\:x^2}}\bigg)$

$\longmapsto\:\tt{\bigg(\dfrac{\pi\:\times\: x^2}{\sqrt{3}\:\times\:x^2}\bigg)}$

$\longmapsto\:\tt{\bigg(\dfrac{\pi\:\times\:\cancel{ x^2}}{\sqrt{3}\:\times\:\cancel{x^2}}\bigg)}$

$\longmapsto\:\tt{\bigg(\dfrac{\pi}{\sqrt{3}}}\bigg)$

$\longmapsto\:\boxed{\boxed{\tt{\dfrac{\pi}{\sqrt{3}}}}}\:\red\bigstar$

$\underline{\boxed {\frak {\therefore \green {Ratio\:of\:their\:areas\:\leadsto\:\pi\:\ratio\:\sqrt{3}}}}}\:\red\bigstar$

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$\underline{\underline{\sf{ \color{magenta}{\qquad Note\:: \qquad} }}}$

Dear user if you are not able to see the diagrams from app. Please see it from the the site (brainly.in). It will be correctly displayed there.

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Answer 2

Step-by-step explanation:

The ratio of the areas of circle and equivalent triangle is par :^3

Given : let ' d' be the diameter of a circle and 'a' be the side of triangle..