If the sides of a triangle are in the ratio 3 | vedclass

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

Question

(B) Let the sides of the triangle be $a = 3k, b = 7k, c = 8k$. The semi-perimeter $s$ is given by $s = \frac{a + b + c}{2} = \frac{3k + 7k + 8k}{2} =

Vedclass · Accepted Answer

$7:2$

Vedclass · Answer

(B) Let the sides of the triangle be $a = 3k, b = 7k, c = 8k$. The semi-perimeter $s$ is given by $s = \frac{a + b + c}{2} = \frac{3k + 7k + 8k}{2} = 9k$. The circumradius $R$ is given by $R = \frac{abc}{4\Delta}$ and the inradius $r$ is given by $r = \frac{\Delta}{s}$,where $\Delta$ is the area of the triangle. Thus,$\frac{R}{r} = \frac{abc}{4\Delta} 	imes \frac{s}{\Delta} = \frac{abc \cdot s}{4\Delta^2}$. Using Heron's formula,$\Delta^2 = s(s-a)(s-b)(s-c) = 9k(9k-3k)(9k-7k)(9k-8k) = 9k(6k)(2k)(k) = 108k^4$. Substituting these values: $\frac{R}{r} = \frac{(3k)(7k)(8k)(9k)}{4(108k^4)} = \frac{1512k^4}{432k^4} = \frac{7}{2}$. Therefore,$R : r = 7 : 2$.

If the sides of a triangle are in the ratio $3 : 7 : 8,$ then $R : r$ is equal to

Similar Questions

In a triangle $ABC$,if $a \neq b$,then the value of $\frac{a \cos A - b \cos B}{a \cos B - b \cos A} + \cos C$ is:

In a $\Delta ABC,$ if $\frac{\sin A}{\sin C} = \frac{\sin (A - B)}{\sin (B - C)},$ then $a^2, b^2, c^2$ are in

With usual notations in $\triangle ABC$,if $a^2+b^2-c^2=ab$,then the measure of angle $C$ is

In $\Delta ABC$,if $2s = a + b + c$,then the value of $\frac{s(s - a)}{bc} - \frac{(s - b)(s - c)}{bc} = $

In a triangle $ABC$,if $a=5, b=3, c=7$,then $\sqrt{\frac{\sin(A-B)}{\sin(A+B)}}=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module