7. ∆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.
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∆ABC is right - angled at A.
so, BC is definitely hypotenuse.
let AB is base and AC is altitude of ∆ABC.
given, AB = 5cm , BC = 13cm and AC = 12cm
now, area of triangle ∆ABC = 1/2 × base × altitude
= 1/2 × length of AB × length of AC
= 1/2 × 5cm × 12cm = 30 cm²
hence, area of ∆ABC = 30cm²
area of ∆ABC = 1/2 × length of AB × length of AC = 1/2 × length of BC × length of AD
=> 5cm × 12cm = 13cm × length of AD
=> 60/13 = length of AD
hence, length of AD = 60/13 cm
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