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# ∆ABC is right angled at A (Fig 11.25). AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, Find the area of ∆ABC. Also find the length of AD.

Q. 7.   $\inline \Delta ABC$ is right angled at $\inline A$  (Fig 11.25). $\inline AD$ is perpendicular to $\inline BC$.  If $\inline AB=5\; cm,$ $\inline BC=13\; cm$ and $\inline AC=12\; cm,$ Find the area of

$\inline \Delta ABC$. Also find the length of$\inline AD$.

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We know that

Area of triangle $= \frac{1}{2} \times base \times height$

Now,

When base = 5 cm and height = 12 cm

Then, the area is equal to

$\Rightarrow \frac{1}{2} \times 5 \times 12 = 30 \ cm^2$

Now,

When base = 13 cm and height = AD area remain same

Therefore,

$\Rightarrow 30= \frac{1}{2} \times 13 \times AD$

$\Rightarrow AD = \frac{60}{13} \ cm$

Therefore, value of AD is  $\frac{60}{3} \ cm$  and the area is equal to $30 \ cm^2$

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