Question

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.

Answer 1

∆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

Answer 2

According to the problem given :

i ) In right angled triangle BAC ,

<A = 90°

AB = 5 cm ,

AC = 12 cm

Area of the right angled triangle

= ( AB × AC )/2

= ( 5 cm × 12 cm )/2

= 5 cm × 6 cm

= 30 square cm ---( 1 )

ii ) In triangle ABC ,

BC perpendicular to AD ,

BC = 13 cm

area of triangle ABC = ( base × altitude )/2

30 sq cm = ( BC × AD )/3

30 = ( 13 × AD )/2

30 × 2 = 13 × AD

60 / 13 = AD

AD ≈ 4.615 square cm

I hope this helps you

:.)