$Δ A B C$ is right angle at A(figure) . AD is perpendicular to BC. if $A B = 5 c m, B C = 13 c m, A C = 12 c m,$ Find the area of $Δ A B C$ . Also find the length of AD.

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Solution

$y = \sqrt{5} = \sqrt{12^{2} - (13 - x)^{2}}$
$5^{2} - x^{2} = 12^{2} - (169 +^{2} - 26 x)$
$\Rightarrow 5^{2} = 12^{2} - 169 + 26 x$
$x = 5 \sqrt{2} c m$
Area $= \frac{1}{2} \times 5 \sqrt{2} \times 13 = \frac{65}{\sqrt{2}} c m^{2}$

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ΔABC is right angle at A(figure) . AD is perpendicular to BC. if AB=5cm,BC=13cm,AC=12cm, Find the area of ΔABC. Also find the length of AD.

y=√5=√122−(13−x)252−x2=122−(169+2−26x)⇒52=122−169+26xx=5√2cmArea =12×5√2×13=65√2cm2

$Δ A B C$ is right angle at A(figure) . AD is perpendicular to BC. if $A B = 5 c m, B C = 13 c m, A C = 12 c m,$ Find the area of $Δ A B C$ . Also find the length of AD.

$y = \sqrt{5} = \sqrt{12^{2} - (13 - x)^{2}}$
$5^{2} - x^{2} = 12^{2} - (169 +^{2} - 26 x)$
$\Rightarrow 5^{2} = 12^{2} - 169 + 26 x$
$x = 5 \sqrt{2} c m$
Area $= \frac{1}{2} \times 5 \sqrt{2} \times 13 = \frac{65}{\sqrt{2}} c m^{2}$