First slide

Equation of line in Straight lines

Question

$In an isosceles triangle O A B, O is the origin and O A = O B = 6 . The equation of the side A B is x - y + 1 = 0 . Then the$
$area of the triangle is$

Moderate

A

$2 \sqrt{21}$
B

$\sqrt{142}$
C

$\frac{\sqrt{142}}{2}$
D

$\frac{\sqrt{71}}{2}$

Solution

$\begin{array}{l} Let D be the mid point of A B . \\ O D = \frac{|c|}{\sqrt{a^{2} + b^{2}}} = \frac{1}{\sqrt{2}} \\ A D = \sqrt{6^{2} - O D^{2}} = \sqrt{36 - \frac{1}{2}} = \sqrt{\frac{71}{2}} \\ ∴ Area of triangle = \frac{1}{2} A B \times O D = \sqrt{\frac{71}{2}} \cdot \sqrt{\frac{1}{2}} = \frac{\sqrt{71}}{2} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App