Question

please solve tjis i am not able to.​

Answer 1

Let the points of the circle on AB and CA be E and F.

Two tangents drawn from one point are equal in length.

Let x be the length of the tangent.

• $\overline{AB}=x+6$ cm
• $\overline{BC}=15$ cm
• $\overline{CA}=x+9$ cm

Properties of inscribed circle.

Area = $\dfrac{1}{2} \times r\times (a+b+c)$ , where $r$ and $(a+b+c)$ are radius and perimeter.

The perimeter of the triangle = $2x+30$ cm.

$\rightarrow\dfrac{1}{2} \times 3\times (2x+30)=54$

$\rightarrow 2x+30=54\times\dfrac{2}{3}$

$\rightarrow 2x+30=36$

$\rightarrow 2x=6$

$\rightarrow x=3$

Hence,

• $\overline{AB}=x+6=3+6=9$ cm
• $\overline{CA}=x+9=3+9=12$ cm

Answer 2

Answer:

AB =9cm

CA=12cm this is the correct answer