In triangle ABC, if a : b : c = 4 : 5 : 6, th | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given $a : b : c = 4 : 5 : 6$. Let $a = 4k, b = 5k, c = 6k$. Semi-perimeter $s = \frac{a+b+c}{2} = \frac{15k}{2}$. Area $\Delta = \sqrt{s(s-a)(s-b

Vedclass · Accepted Answer

$16 : 7$

Vedclass · Answer

(A) Given $a : b : c = 4 : 5 : 6$. Let $a = 4k, b = 5k, c = 6k$. Semi-perimeter $s = \frac{a+b+c}{2} = \frac{15k}{2}$. Area $\Delta = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{15k}{2}(\frac{7k}{2})(\frac{5k}{2})(\frac{3k}{2})} = \frac{15\sqrt{7}k^2}{4}$. Circumradius $R = \frac{abc}{4\Delta} = \frac{120k^3}{4 	imes \frac{15\sqrt{7}k^2}{4}} = \frac{8k}{\sqrt{7}}$. Inradius $r = \frac{\Delta}{s} = \frac{15\sqrt{7}k^2}{4} 	imes \frac{2}{15k} = \frac{\sqrt{7}k}{2}$. Ratio $\frac{R}{r} = \frac{8k}{\sqrt{7}} 	imes \frac{2}{\sqrt{7}k} = \frac{16}{7}$.

In $\triangle ABC$, if $a : b : c = 4 : 5 : 6$, then the ratio of the circumradius to its inradius is

Similar Questions

In a $\triangle ABC$,if $\frac{2 r_2 r_3}{r_2-r_1}=r_3-r_1$,then $\frac{r_1(r_2+r_3)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} = $

In $\Delta ABC$,$AB = AC$. Let $P_1$ denote the incircle of $\Delta ABC$. Circle $P_2$ is tangent to sides $AB$,$AC$ and to circle $P_1$. If the radii of circles $P_1$ and $P_2$ are $2$ and $1$ respectively,then the area of $\Delta ABC$ is:

In an equilateral triangle of side $2\sqrt{3} \text{ cm}$,the circum-radius is ..... $\text{cm}$.

In $\triangle ABC$,if $a: b: c = 4: 5: 6$,then the ratio between the circumradius and the inradius is

The difference between the areas of the circumcircle and the incircle of a regular decagon of side $2 \, cm$ is -

Vedclass Test Series

Exam Paper Generator

Online Exam Module