∆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.

In right angles triangle BAC, AB = 5 cm and AC = 12 cm
Area of triangle = 1/2 x base x height = 1/2 x AB x AC
= 1/2 x 5 x 12 = 30 cm²
Now, in ∆ABC
Area of triangle ABC = 1/2 x BC x AD
⇒ 30 = 1/2 x 13 x AD
⇒ AD = 30×2/13 = 60/13

Class 7 Maths Chapter 11 Exercise 11.2

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