Two sides of a triangle are given by the root | vedclass

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

Question

(D) The given equation is $x^2-5x+6=0$. \ Solving for $x$: $(x-3)(x-2)=0$,which gives $x=3$ and $x=2$. \ Let the two sides be $a=3$ and $b=2$,and th

Vedclass · Accepted Answer

$5+\sqrt{7}$

Vedclass · Answer

(D) The given equation is $x^2-5x+6=0$. \ Solving for $x$: $(x-3)(x-2)=0$,which gives $x=3$ and $x=2$. \ Let the two sides be $a=3$ and $b=2$,and the included angle be $C=\frac{\pi}{3}$. \ Using the Law of Cosines: $\cos C = \frac{a^2+b^2-c^2}{2ab}$. \ Substituting the values: $\cos(\frac{\pi}{3}) = \frac{3^2+2^2-c^2}{2 	imes 3 	imes 2}$. \ $\frac{1}{2} = \frac{9+4-c^2}{12} \Rightarrow \frac{1}{2} = \frac{13-c^2}{12}$. \ $6 = 13-c^2$ $\Rightarrow c^2 = 7$ $\Rightarrow c = \sqrt{7}$. \ The perimeter of the triangle is $a+b+c = 3+2+\sqrt{7} = 5+\sqrt{7}$.

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is

Similar Questions

Which of the following biomolecules is common to respiration-mediated breakdown of fats,carbohydrates and proteins?

If a bar magnet of pole strength $m$ and magnetic moment $M$ is cut equally $5$ times parallel to its axis and again $3$ times perpendicular to its axis,then the pole strength and magnetic moment of each piece are respectively

$A$ $10 \mu F$ capacitor is charged by a $100 \text{ V}$ battery. It is disconnected from the battery and is connected to another uncharged capacitor of capacitance $30 \mu F$. During this process,the electrostatic energy lost by the first capacitor is

Gonadotropic hormones are produced by .....

Let $\alpha, \beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2}, 2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of $r$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module