Question

The sides of a triangle are in A.P and its area is $\left(3/5\right)\times$ (area of an equilateral triangle of the same perimeter) then is area of the $\Delta$le is

• A. $\frac{\sqrt{3}}{20}{b}^2$
• B. $\frac{3\sqrt{3}}{20}{b}^2$
• C. $\frac{3\sqrt{3}}{20}{\left(\frac{a+b}{3}\right)}^2$
• D. $\frac{3\sqrt{3}}{20}{a}^2$

Answer 1

The correct option is D $\frac{3\sqrt{3}}{20}{a}^2$

Let the sides be $a-x,a,a+x$

$\therefore$ perimeter $=a-x+a+a+x=3a$

$\therefore$ side of Equilateral $\Delta le$ with perimeter $3a$

$=\frac{3a}{3}=a$

Area of Equilateral $\Delta le=\frac{\sqrt{3}}{4}\times a^2$

with side $a$

Area of $\Delta le$ with side in $A.P$

$=\frac{3}{5}\times \frac{\sqrt{3}}{4}{a}^2$

$=\frac{3\sqrt{3}}{20}{a}^2$

In Question it is mentioned what is $a$ & what is $b$