Relationship between a Perimeter and Area

Geometry Level 2

The relationship between the area $A$ of an equilateral triangle and its perimeter $P$ is given by the formula $A = kP^2$ , where $k$ is a constant. What is the value of $k$ ?

\frac{1}{9}

\frac{1}{2}

\frac{\sqrt{3}}{36}

\sqrt{3}

\frac{\sqrt{3}}{4}

1 solution

Marta Reece
Jun 22, 2017

$A=\dfrac{\sqrt3}4a^2$

$P^2=(3a)^2=9a^2$

$A=kP^2$

$\dfrac{\sqrt3}4a^2=k\times9a^2$

$k=\dfrac{\sqrt3}{4\times9}=\boxed{\dfrac{\sqrt3}{36}}$

Thank you.

Hana Wehbi - 3 years, 11 months ago

Relationship between a Perimeter and Area

1 solution

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