ΔABC is right-angled at A. AD is perpendicular to BC, AB = 5cm, BC = 13 cm and AC = 12 cm. Find the area of ΔABC. Also, find the length of AD.

∆ABC is right – angled at A. so, BC is definitely hypotenuse.

let AB is base and AC is altitude of ∆ABC.

Given, AB = 5 cm , BC = 13 cm and AC = 12 cm

now, area of triangle ∆ABC = 1/2 × base × altitude

= 1/2 × length of AB × length of AC

= 1/2 × 5 cm × 12 cm = 30 cm²

hence, area of ∆ABC = 30 cm²

area of ∆ABC = 1/2 × length of AB × length of AC

= 1/2 × length of BC × length of AD

⇒ 5 cm × 12 cm = 13 cm × length of AD

⇒ 60/13 = length of AD

hence, length of AD

= 60/13 cm

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