Question

calculate the area of triangle whose sides are 18 cm 24 cm and 30 cm in length also find the length of altitude corresponding to the smallest side

Answer 1

Find the semi-perimeter:

p = (18 + 24 + 30) ÷ 2 = 36 cm

Find the area of the triangle:

area = √p(p-a)(p-b)(p-c)

area = √36(36 - 18)(36 - 24)(26 - 30)

area = √46656

area = 216 cm²

Find the length of the altitude corresponding to the smallest side:

area = 1/2 (base) (height)

216 = 1/2 (18) (height)

216 = 9 height

height = 216 ÷ 9 = 24 cm

Answer: The area is 216 cm² and the corresponding height is 24 cm

Answer 2

$\color{red}{ \bold{ \huge{ \boxed{thanks \: for \: asking \: this \: question}}}}$


$\bold{ \huge{ \boxed{good \: morning}}}$


$\color{indigo}{ \bold{ \huge{ \boxed{required \: answer}}}}$



$\bold{ \underline{area \: of \: semi - triangle}}$

$\bold{ \underline{ \boxed{18 + 24 + 30 = \frac{72}{2} = 36}}}$
$\bold{ \underline{ \boxed{now}}}$

$\bold{ \underline{ \boxed{ \sqrt{y(y - a)(y - b)(y - c)}}}}$


$\bold{ \underline{ \boxed{ \sqrt{36(36 - 18)(36 - 24)(36 - 30)}}}}$
$\bold{ \underline{ \boxed{ \sqrt{36(18)(24)(30)}}}}$

$\bold{ \underline{ \boxed{ \sqrt{46656}}}}$

$\bold{ \underline{ \boxed{ =) 216}}}$


$\bold{ \underline{ \boxed{again}}}$


$\bold{ \underline{ \boxed{area \: of \: triangle = \frac{1}{2} \times base \times height}}}$


$\bold{ \underline{ \boxed{ 216 = \frac{1}{2} \times 18 \times h}}}$


$\bold{ \underline{ \boxed{216 \times 2 = 18h}}}$

$\bold{ \underline{ \boxed{h = \frac{216 \times 2}{18}}}}$

$\bold{ \underline{ \boxed{h = \frac{432}{18} = )24}}}$


$\color{red}{\bold{ \underline{ \boxed{therefore}}}}$

$\bold{ \underline{ \boxed{height = 24}}}$