Question

The length of sides of triangle is 7cm, 13cm and 12cm. Find the length of perpendicular from vertex to side whose length is 12cm.

Answer 1

Answer:

4√3 cm

Step-by-step explanation:

Area of triangle by Heron formula = √s(s-a)(s-b)(s-c) where s=a+b+c/2

s=7+13+12/2=16

=√16(16-7)(16-13)(16-12)

=√16(9)(3)(4)

=√2×2×2×2×3×3×3×2×2

=24√3cm^2

Area of triangle=1/2×base×height

24√3=1/2×12×h

24√3=6h

24√3/6=h

4√3=h

h=4√3cm

Answer 2

Answer:

length of the triangle is 7cm, 13cm, and 12 cm(base).

perimeter of the triangle: 7+13+12=32cm

semi-permeter(s):32/2=16cm

Area=√s(s-a)(s-b)(s-c)

= √16(16-7)(16-13)(16-12)

=√16*9*3*4

=√2*2*2*2*3*3*3*2*2

=2*2*3*2√3

=24√3 sq.cm

perpendicular or height(h):

1/2*12*h=24√3

6*h=24√3

h=24√3/6

h=4√3 cm

Ans. The perpendicular from vertex to side whose length is 12 cm is 4√3 cm.