Question

The sides of one regular hexagon is larger than that of the other regular hexagon by one cm. If the product of their areas is $243$, then find the sides of the regular hexagons.

• A. $2cm,3cm$
• B. $3cm,4cm$
• C. $1cm,2cm$
• D. $4cm,5cm$

Answer 1

The correct option is A $2cm,3cm$

Area of Hexagon $=\frac{3\sqrt{3}}{2}{a}^2$

Let the side of the hexagon be $a,a+1$

Now, $243=\frac{3\sqrt{3}}{2}{a}^2.\frac{3\sqrt{3}}{2}(a+1{)}^2\Rightarrow 243=\frac{27}{4}{a}^2(a+1{)}^2\Rightarrow 9\ast 4=a^2(a+1{)}^2\Rightarrow a(a+1)=6\Rightarrow a^2+a-6=0\Rightarrow a=2,3$