Question

9. Find the area of the triangle if the perimeter of the triangle is 32 cm and the
sides of the triangle are 8 cm, 11 cm, 13 cm​

Answer 1

Answer:

$\huge\underline\bold \red{solution -}$

$\bold{perimeter \: = \: 32cm}$

Lᴇᴛ ᴛʜᴇ sɪᴅᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ʙᴇ a,b,c.

$\bold{a \: = \: 8cm}$

$\bold{b \: = \: 11cm}$

$\bold{c \: = \: 13cm}$

$\underline \bold \green{by \: using \: herons \: formula - }$

$\bold{semiperimeter(s) \: = \: \frac{32}{2}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ = \: 16cm}$

$\bold{area \: = \sqrt{s(s - a) \: (s - b) \: (s - c)}}$

$\bold{ = \sqrt{16(16 - 8) \: (16 - 11) \: (16 - 13)}}$

$\bold{ = \sqrt{16 \times 8 \times 5 \times 3}}$

$\bold{ = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 3}}$

$\underline\bold \pink{answer = 8 \sqrt{30}....}$

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