In Δ ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of Δ ABC is 30 cm 2 and R and r are respectively the radii of circumcircle and incircle of Δ ABC, then the value of 2 R + r (in cm ) is equal to .

Question

In Δ ABC, the lengths of sides AC and AB are 12 cm and 5 cm, respectively. If the area of Δ ABC is 30 cm 2 and R and r are respectively the radii of circumcircle and incircle of Δ ABC, then the value of 2 R + r (in cm ) is equal to . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a08348f9163dc46a89dc7b846a22cbe7-.png" /> Δ=(1/2) ⋅ 5.12 ⋅ sin A =30 sin A =1 A =90° ⇒ BC =13 BC =2 R =13 r =(Δ/ S )=(30/15)=2 2 R + r =15

Q. In $Δ A BC$ , the lengths of sides $A C$ and $A B$ are $12 c m$ and $5 c m$ , respectively. If the area of $Δ A BC$ is $30 c m^{2}$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $Δ A BC$ , then the value of $2 R + r$ (in $c m$ ) is equal to ________.

$Δ = \frac{1}{2} \cdot 5.12 \cdot sin A = 30$
$sin A = 1$
$A = 9 0^{\circ} \Rightarrow BC = 13$
$BC = 2 R = 13$
$r = \frac{Δ}{S} = \frac{30}{15} = 2$
$2 R + r = 15$

Q. In ΔABC, the lengths of sides AC and AB are 12cm and 5cm, respectively. If the area of ΔABC is 30cm2 and R and r are respectively the radii of circumcircle and incircle of ΔABC, then the value of 2R+r (in cm ) is equal to ________.

Δ=21​⋅5.12⋅sinA=30 sinA=1 A=90∘⇒BC=13 BC=2R=13 r=SΔ​=1530​=2 2R+r=15

Q. In $Δ A BC$ , the lengths of sides $A C$ and $A B$ are $12 c m$ and $5 c m$ , respectively. If the area of $Δ A BC$ is $30 c m^{2}$ and $R$ and $r$ are respectively the radii of circumcircle and incircle of $Δ A BC$ , then the value of $2 R + r$ (in $c m$ ) is equal to ________.

$Δ = \frac{1}{2} \cdot 5.12 \cdot sin A = 30$
$sin A = 1$
$A = 9 0^{\circ} \Rightarrow BC = 13$
$BC = 2 R = 13$
$r = \frac{Δ}{S} = \frac{30}{15} = 2$
$2 R + r = 15$