Question

A $△ABC$ in which $AB=5.4\text{cm},\angle CAB={45}^{\circ }$ and $AC+BC=9\text{cm}$. Then, perimeter of $\Delta ABC$ is

• A. $14.4\text{cm}$
• B. $11.4\text{cm}$
• C. $12.4\text{cm}$
• D. $15.4\text{cm}$

Answer 1

The correct option is A $14.4\text{cm}$

$\Rightarrow$ Draw line segment $AB=5.4cm$

$\Rightarrow$ Take $A$ as center and draw angle of ${45}^o$

$\Rightarrow$ Cut off $AD=9cm$

$\Rightarrow$ Join $BD$

$\Rightarrow$ Now, draw perpendicular bisector of $BD$ which

intersect $AD$ at point $C$.

$\Rightarrow$ Now join $CB$

$\Rightarrow$ Measure the length of $AC$ and $BC$

$\Rightarrow$ We get $AC=5cm$ and $BC=4cm$

$\Rightarrow$ Perimeter of $△ABC=5.4+4+5=14.4cm$