Question

Find the ratio of the area to the perimeter of an acute triangle as shown in figure.

• A. $\frac{7}{9}$
• B. $\frac{9}{7}$
• C. $\frac{7}{9}$
• D. $\frac{2}{3}$
• E. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{7}{9}$

Given,
Base of a triangle$=BC=7$
Height of a triangle$=AD=4$
Let's consider a triangle $△ABC$ as shown.
Here $BC=7$ and $AD=4$

As we know,
Area of$△ABC=\frac{1}{2}\times \text{Base}\times \text{Height}$
$\Rightarrow \frac{1}{2}\times 7\times 4=14$ sq. unit.

$\to$Perimeter of the triangle.
Perimeter of the triangle = sum of all three sides of a traingle.
$=AB+BC+AC$
$=5+7+6=18$ unit.

Hence the ratio is,
$\frac{\text{Area of triangle ABC}}{\text{Perimeter of the triangle ABC}}=\frac{14}{18}=\frac{7}{9}$