If the sides of the triangle are 5K, 6K, 5K a | vedclass

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

Question

(A) Let the sides of the triangle be $a = 5K$,$b = 6K$,and $c = 5K$.The semi-perimeter $s$ is given by $s = \frac{a + b + c}{2} = \frac{5K + 6K + 5K}{

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) Let the sides of the triangle be $a = 5K$,$b = 6K$,and $c = 5K$.The semi-perimeter $s$ is given by $s = \frac{a + b + c}{2} = \frac{5K + 6K + 5K}{2} = \frac{16K}{2} = 8K$.The area of the triangle $\Delta$ using Heron's formula is $\Delta = \sqrt{s(s - a)(s - b)(s - c)}$.Substituting the values: $\Delta = \sqrt{8K(8K - 5K)(8K - 6K)(8K - 5K)} = \sqrt{8K 	imes 3K 	imes 2K 	imes 3K} = \sqrt{144K^4} = 12K^2$.The radius of the incircle $r$ is given by $r = \frac{\Delta}{s}$.Given $r = 6$,we have $6 = \frac{12K^2}{8K}$.Simplifying the expression: $6 = \frac{3K}{2}$.Therefore,$3K = 12$,which gives $K = 4$.

If the sides of the triangle are $5K, 6K, 5K$ and the radius of the incircle is $6$,then the value of $K$ is equal to

Similar Questions

If $\alpha, \beta, \gamma$ are the lengths of the tangents from the vertices of a triangle to its incircle,then:

In $\triangle ABC$,if $r=1, R=4$ and $\Delta=8$,then $\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}=$

In triangle $ABC$,if $a=6, b=8$ and $c=10$,then $\frac{2 r_2 r_3}{r r_1} = $

In $\triangle ABC$,the circle that touches the side $BC$ internally and the other two sides $AB$ and $AC$ externally is called:

Let $ABC$ be a scalene triangle with incentre $I$ and circumcentre $O$. Suppose $B, C, I, O$ are concyclic points. Then $\angle B + \angle C$ is (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module