Question

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

Answer 1

Hᴇʀᴇ's Yᴏᴜʀ Aɴsᴡᴇʀ:-

Lᴇᴛ Tʜᴇ Sɪᴅᴇs ᴏғ Tʜᴇ Tʀɪᴀɴɢʟᴇ ʙᴇ a, b Aɴᴅ c.

Gɪᴠᴇɴ Lᴇɴɢᴛʜ ᴏғ Tʜᴇ Sɪᴅᴇs ᴏғ Tʜᴇ Tʀɪᴀɴɢʟᴇ Aʀᴇ:-

a = 8 cm

b = 11 cm

c = ?

Pᴇʀɪᴍᴇᴛᴇʀ ᴏғ Tʜᴇ Tʀɪᴀɴɢʟᴇ ɪs Gɪᴠᴇɴ = 32 cm.

Sɪɴᴄᴇ Tʜᴇ Sᴜᴍ ᴏғ Aʟʟ Tʜʀᴇᴇ Sɪᴅᴇs ᴏғ ᴀ Tʀɪᴀɴɢʟᴇ ɪs Iᴛs Pᴇʀɪᴍᴇᴛᴇʀ

⇏a + b + c = 32 cm

⇏8 + 11 + c = 32 cm

⇏19 + c = 32 cm

⇏c = 13 cm

Nᴏᴡ ᴡᴇ Wɪʟʟ Fɪɴᴅ Tʜᴇ Aʀᴇᴀ ᴏғ Tʜᴇ Tʀɪᴀɴɢʟᴇ ʙʏ Hᴇʀᴏɴ's Fᴏʀᴍᴜʟᴀ Wʜɪᴄʜ ɪs √s ( s - a )( s - b )( s - c ) Wʜᴇʀᴇ s ɪs Tʜᴇ Sᴇᴍɪ Pᴇʀɪᴍᴇᴛᴇʀ ᴏғ Tʜᴇ Tʀɪᴀɴɢʟᴇ.

Sᴇᴍɪ Pᴇʀɪᴍᴇᴛᴇʀ ᴏғ Tʜɪs Tʀɪᴀɴɢʟᴇ = 32/2 = 16 cm.

Aʀᴇᴀ ᴏғ Tʜᴇ Tʀɪᴀɴɢʟᴇ = √s ( s - a )( s - b )( s - c )

⇏√( 16 × 8 × 5 × 3 )

⇏√( 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3 )

⇏2 × 2 × 2√( 2 × 5 × 3 )

⇏8√30 cm².

Hᴏᴘᴇ ɪᴛ Hᴇʟᴘs ᴜʜ....

Answer 2

✿Given:-

•Two Sides Of Traingle Are 8cm , 11 cm and perimeter is 32 Cm

✿Find :-

•Area Of Triangle

✿Let's Slove✿

A=11 Cm,B=8 Cm,2s=32

A + B + C = 2s

8 + 11+ c = 2s

C = 13

✿Therefore,

s-a = 16-8=8

s-b=16-11=5

s-c=16-13=3

✿Hence, Area Of Given Triangle:-

s(s-a) ×(s-b) ×(s-c)

16×8×5×3=

$8 \sqrt{30} {cm}^{2}$

✿Hence Solved

Keep On Answering✿