Question

Find the area of triangle, two sides of which are 8 cm and 11 cm, the perimeter is 32 cm.

Answer 1

Answer:

perimeter = sum of all sides

32cm = 8 +11 +x

32 = 19 + x

32-19 =x

13cm = x

so the third side is 13cm

(you cant find out the area by 1/2 ×base× height bcz height is not given so in this case we will apply heron's formula)

herons formula =

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

s = a+b+c /2 (a,b and c are three sides of triangle)

s= 8+11+13 /2

s=32/2

s= 16

root( 16-8) (16-11) (16-13)

root (8)(5)(3)

root 2×2×2×5×3 ( take 2 ×2 outside of root )

2root2×5×3

2root30 ans ( ye area h)

root mene likha but aap root lagana mat bhoolna it is important..... :)

Answer 2

Given :

⬤ Two Sides of Triangle are 8 cm and 11 cm .

⬤ Perimeter of Triangle is 32 cm .

To Find :

⬤ Area of Triangle .

Solution :

• Side a = 8 cm
• Side b = 11 cm
• Side c = x

First , We have to Calculate Value of Side C . Hence ,

a + b + c = 32

8 + 11 + c = 32

19 + c = 32

c = 32 - 19

c = 13

Therefore , The Value of Side c is 13 .

So ,

• Side a = 8 cm .
• Side b = 11 cm .
• Side c = 13 cm .

s = a + b + c/2

s = 8 + 11 + 13/2

s = 32/2

s = 16

Therefore , The Semi Perimeter is 16 cm .

Now :

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

= √16(16 - 8) (16 - 11) (16 - 13)

= √16 × 8 × 5 × 3

= 8√30

Therefore , The Area of Triangle is 8√30 cm² .