First slide

Equation of line in Straight lines

Question

In an isosceles triangle $OAB, O$ is the origin and $OA = OB = 6$ . The equation of the side AB is $x - y + 1 = 0 .$ The area of triangle is

Moderate

A

$2 \sqrt{21}$
B

$\sqrt{142}$
C

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

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

Solution

Let D be the midpoint of AB.
$OD = \frac{1}{\sqrt{2}}$
$AD = \sqrt{6^{2} - {OD}^{2}} = \sqrt{36 - \frac{1}{2}} = \sqrt{\frac{71}{2}}$
$∴$ Area of triangle $= \frac{1}{2} \times AB \times OD = \sqrt{\frac{71}{2}} \times \sqrt{\frac{1}{2}} = \frac{\sqrt{71}}{2}$

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