Question
Two mutually perpendicular straight lines through the origin from an isosceles triangle with the line $2x + y = 5$ . Then the area of the triangle is :
✓
Answer
a
$A D=\left|\frac{0+0-5}{\sqrt{(2)^{2}+(1)^{2}}}\right| \Rightarrow \frac{5}{\sqrt{5}} \Rightarrow \sqrt{5}$
$A D=\left|\frac{0+0-5}{\sqrt{(2)^{2}+(1)^{2}}}\right| \Rightarrow \frac{5}{\sqrt{5}} \Rightarrow \sqrt{5}$
$In$ triangle $A B D$
$\tan 45^{\circ}=\frac{A D}{B D} \Rightarrow \frac{\sqrt{5}}{B D}=1$
$B D=\sqrt{5}$
$DC=\sqrt{5}$
$BC=2 \sqrt{5}$
Area of $\Delta A B C=\frac{1}{2} \times B C \times A D \Rightarrow \frac{1}{2} \times 2 \sqrt{5} \times \sqrt{5}$$=5$
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