Question

Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.

Answer 1

Hey friend,
Here is the answer you were looking for:

Given that 2 sides of triangles are 18cm and 10cm

And perimeter = 42cm

We know that perimeter = a + b + c

Let a = 18cm
b = 10cm

So,
42cm = 18cm + 10cm + c
42 - (18 + 10) = c

c = 42 - 28

c = 14cm

So,
Semi-perimeter = perimeter/2
s = 42/2
s = 21cm

Now,
Area of Triangle (According to Heron's Formula)

= √[s(s - a)(s - b)(s - c)]

Putting the values :

$\sqrt{21(21 - 18)(21 - 10)(21 - 14)} \\ \\ = \sqrt{21(3)(11)(7)} \\ \\ = \sqrt{4851} \\ \\ = 69.64 {cm}^{2} \: (approx)$

Hope this helps!!

If you have any doubt regarding to my answer, feel free to ask in the comment section or inbox me if needed.

@Mahak24

Thanks...
☺☺

Answer 2

Perimeter of a triangle=a+b+c
42=18+10+c
42-28=c
14=c
C=14cm
Semi Perimeter=perimeter/2
S=42/2
S=21cm
$\sqrt{21(21 - 18)(21 - 10)(21 - 14)}$
$\sqrt{21(3)(11)(7)}$
$\sqrt{3 \times 7 \times 3 \times 11 \times 7}$

$3 \times 7 \sqrt{11}$
$21 \sqrt{11}$