Two sides of a triangle have lengths a text{ | vedclass

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

Question

(A) Let the two sides of the triangle be $a$ and $b$,and the angle between them be $	heta$.The area of the triangle is given by $A = \frac{1}{2}ab \s

Vedclass · Accepted Answer

$\frac{1}{2}\sqrt{a^2 + b^2}$

Vedclass · Answer

(A) Let the two sides of the triangle be $a$ and $b$,and the angle between them be $	heta$.The area of the triangle is given by $A = \frac{1}{2}ab \sin	heta$.For the area to be maximum,$\sin	heta$ must be maximum,which occurs when $	heta = 90^\circ$.Thus,the triangle is a right-angled triangle with sides $a$ and $b$ forming the right angle.Let the vertex containing sides $a$ and $b$ be at the origin $(0,0)$ in the Cartesian plane.The coordinates of the vertices are $(0,0)$,$(a,0)$,and $(0,b)$.The midpoint of the hypotenuse (the side opposite to the right angle) is $M = (\frac{a}{2}, \frac{b}{2})$.The median from the vertex $(0,0)$ to the hypotenuse is the distance from $(0,0)$ to $M$.Length of the median $m = \sqrt{(\frac{a}{2} - 0)^2 + (\frac{b}{2} - 0)^2} = \sqrt{\frac{a^2}{4} + \frac{b^2}{4}} = \frac{1}{2}\sqrt{a^2 + b^2}$.

Two sides of a triangle have lengths $a \text{ cm}$ and $b \text{ cm}$. If the triangle is to have the maximum area,then the length of the median from the vertex containing the sides $a$ and $b$ is

Similar Questions

If a straight line perpendicular to $2x - 3y + 7 = 0$ forms a triangle with the coordinate axes whose area is $3 \text{ sq. units}$,then the equation of the straight line is:

The acute angle between the diagonals of a parallelogram whose vertices are $A(2, -1), B(0, 2), C(2, 3)$ and $D(4, 0)$ is

The circumcenter of the triangle formed by the lines $xy + 2x + 2y + 4 = 0$ and $x + y + 2 = 0$ is

The area (in square units) of the triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ is:

In $\triangle ABC$,the coordinates of the vertex $A$ are $(-3, 1)$. If the equation of the median through $B$ is $2x + y - 3 = 0$ and the equation of the angle bisector of $\angle C$ is $7x - 4y - 1 = 0$,then the equation of the side $BC$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module