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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.   \Delta 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 

           \Delta ABC. Also find the length ofAD.

          

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R Riya

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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