Question

find the area of a triangular field of sides 18m, 24m , and 30.also find the altitude corresponding to the shortest side

Answer 1

Hope this is correct

Answer 2

Answer:

The area of the triangle is 216 square meters

The altitude corresponding to the shortest side is of length 24 m

Step-by-step explanation:

Sides of triangle :

a = 18

b =24

c = 30

To calculate the area of given triangle we will use the heron's formula :

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

Where $s = \frac{a+b+c}{2}$

a,b,c are the side lengths of triangle

Now substitute the values :

$s = \frac{18+24+30}{2}$

$s =36$

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

$Area = 216$

Hence the area of the triangle is 216 square meters

Now the length of the shortest side is 18 m

Now to find the  altitude corresponding to the shortest side

So, formula of area of triangle $=\frac{1}{2} \times Base \times Height$

Since Area = 216 square meters

So,$216 =\frac{1}{2} \times 18\times Height$

$216 =9 \times Height$

$\frac{216}{9}=Height$

$24=Height$

Thus the altitude corresponding to the shortest side is of length 24 m