Question

In ABC, AD is the perpendicular to BC. If AB=6cm, BC=10cm and AC=8cm. Find the area of the
triangle. Also find the length of AD.

Answer 1

Given:

In ABC, AD is perpendicular to BC. If AB=6cm, BC=10cm and AC=8cm

To Find:

Area of the  triangle and also the length of AD

Solution:

Let AB=a, BC=b, and CD=c

By Heron's Formula,

Area of a triangle = √s(s - a)(s - b)(s- c).......(i)

where s = 1/2(a+b+c)

             = 1/2(6+10+8)= 1/2 x24 = 12cm

So, area of triangle   = √12(12-6)(12-10)(12-8)

                                  = √12x 6 x2 x4 = 24cm²

Also, area of triangle = 1/2(base x height)

                            24   = 1/2 (10 x height)

                            24   = 5 x AD

⇒                      AD = (24/5) = 4.8cm

Hence, the length of AD is 4.8cm

Answer 2

Answer:

4.8 cm

Step-by-step explanation:

steps are given in the photo

kindly refer it

without heron formula