Triangle ABC is right angled at a a d is perpendicular to BC if a b is equal to 5 cm BC is equal to 13 cm and ac is equal to 12 cm find the area of triangle ABC and also length of a d
Answers
Answered by
1
In ∆ABC,
p = 5+13+12 = 30cm
s = p/2 = 15cm
thus, by heron's formula
area(∆ABC) = √s(s-a)(s-b)(s-c)
= √15(15-5)(15-13)(15-12)
= √5×3×5×2×2×3
= 5×3×2 = 30cm²
BD = BC (since : AD is perpendicular)
BD = BC = 13/2 = 6.5cm
In ∆ADC,
by Pythagoras theorem,
AC² = DC² + AD²
12² = 6.5² + AD²
144 = 42.25 + AD²
144 - 42.25 = AD²
√101.75 = √AD²
AD = 10.08 cm
p = 5+13+12 = 30cm
s = p/2 = 15cm
thus, by heron's formula
area(∆ABC) = √s(s-a)(s-b)(s-c)
= √15(15-5)(15-13)(15-12)
= √5×3×5×2×2×3
= 5×3×2 = 30cm²
BD = BC (since : AD is perpendicular)
BD = BC = 13/2 = 6.5cm
In ∆ADC,
by Pythagoras theorem,
AC² = DC² + AD²
12² = 6.5² + AD²
144 = 42.25 + AD²
144 - 42.25 = AD²
√101.75 = √AD²
AD = 10.08 cm
Similar questions