Question

The ratio of the sides lenghts of a triangle is 3:6:8, and it's perimeter is 136 cm what is the length of the shortest side,in cm

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Thissumisfromchapter−Quadrilaterals
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\large\underline\bold\red{Given:-}
Given:−
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✯ ᴛʜᴇ ʀᴀᴛɪᴏ ᴏꜰ ᴛʜᴇ ꜱɪᴅᴇꜱ ʟᴇɴɢᴛʜ ᴏꜰ ᴀ ᴛʀɪᴀɴɢʟᴇ ɪꜱ 3:6:8, ᴀɴᴅ ɪᴛ'ꜱ ᴘᴇʀɪᴍᴇᴛᴇʀ ɪꜱ 136 ᴄᴍ ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴛʜᴇ ꜱʜᴏʀᴛᴇꜱᴛ ꜱɪᴅᴇ, ɪɴ ᴄᴍ.

\large\underline\bold\red{To\:Find:-}
ToFind:−
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✯ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴛʜᴇ ꜱʜᴏʀᴛᴇꜱᴛ ꜱɪᴅᴇ, ɪɴ ᴄᴍ.

\large\underline\bold\red{Solution:-}
Solution:−
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✯ ʟᴇᴛ ᴛʜᴇ ꜱɪᴅᴇꜱ ᴏꜰ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ʙᴇ 3x, 6x ᴀɴᴅ 8x ʀᴇꜱᴘᴇᴄᴛɪᴠᴇʟʏ

✯ ᴛʜᴇɴ,

☞ 3x + 6x + 8x = 136

☞ 17x = 136

☞ x = \sf\frac{136}{17}
17
136
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☞ x = {\small{\boxed{\red{8}}}}
8
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\implies⟹ ꜱʜᴏʀᴛᴇꜱᴛ ꜱɪᴅᴇ = 3x

⠀⠀ㅤㅤ⠀⠀ ⠀⠀ㅤ⠀ ⠀= (3 × 8) ᴄᴍ

⠀⠀ㅤㅤ⠀⠀ ⠀⠀ㅤ⠀ ⠀= 24 ᴄᴍ​

Answer 1

Answer :

24 cm

Step - by - step explanation :

Perimeter of the triangle = 136 cm

Ratio of the sides of a triangle = 3:6:8

Let the length sides of the triangle be 3x , 6x and 8x respectively .

According to the question ,

3x + 6x + 8x = 136 cm

or, 17x = 136 cm

or, x = 136 / 17 cm

or, x = 8 cm

Now ,

3x = 3 × 8 cm = 24 cm ,

6x = 6 × 8 cm = 48 cm

and , 8 × 8 cm = 64 cm

Therefore , the shortest side of the triangle is 24 cm