Question

calculAte area of triangle whose sides are 18 ,24,30 find length of altitude corresponding to smallest side

Answer 1

Explanation:

Using Heron's formula

s = (18+24+30)/2 = 36

Area =

$\sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{36(36 - 18)(36 - 24)(36 - 30)}$

$= \sqrt{36 \times 18 \times 12 \times 6}$

$= \sqrt{18 \times 2 \times 18 \times 6 \times 2 \times 6}$= 18 x 2 x 6

= 216 sq.units

Now, Area of triangle = 1/2 x Base x Height

Smallest side is 18

To find: Altitude (h)

$= > 216 = \frac{1}{2} \times 18 \times h$

$= > h = \frac{216 \times 2}{18} = 24$