Question

the sides of the triangle are in the ratio 1/3: 1/4: 1/5 are its perimeter is 94cm.the length of the smallest side is ?
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Answer 1

Given:

The sides of a triangle are in the ratio (1/3):(1/4):(1/5)

The perimeter of the triangle is 94 cm

To find:

The length of the smallest side of the triangle

Now,

Let the side of the triangle be

• (1/3)x = (x/3) cm
• (1/4)x = (x/4) cm
• (1/5)x = (x/5) cm

The perimeter of the triangle = Sum of all sides of the triangle

$\implies \frac{x}{3}+ \frac{x}{4}+ \frac{x}{5} = 94$

$\implies \frac{20x+15x+12x}{60} = 94$

$\implies 20x+15x+12x = 94 \times\bf{ 60}$

[Taking 60 to RHS]

$\implies 47x= 5640$

$\implies x= \frac{5640}{47}$

∴ x = 120

So,

The sides of the triangle are

• (1/3)x = (x/3) cm

= (120)/3 = 40 cm

• (1/4)x = (x/4) cm

= (120)/4 = 30 cm

• (1/5)x = (x/5) cm

= (120)/5 = 24 cm

Hence,

• The smallest side is 24 cm

Answer 2

GIVEN :-

• Tʜᴇ sɪᴅᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇ ɪɴ ᴛʜᴇ ʀᴀᴛɪᴏ $\bf\red{\dfrac{1}{3}\::\:\dfrac{1}{4}\::\:\dfrac{1}{5}\:}$ .

• Tʜᴇ ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ɪs "94 ᴄm" .

TO FIND :-

• Tʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ sᴍᴀʟʟᴇsᴛ sɪᴢᴇ ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ .

SOLUTION :-

ʟᴇᴛ,

• ᴛʜᴇ sɪᴅᴇs ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ʙᴇ,

1. $\bf{\dfrac{X}{3}\:cm\:}$

2. $\bf{\dfrac{X}{4}\:cm\:}$

3. $\bf{\dfrac{X}{5}\:cm\:}$

ᴡᴇ ʜᴀᴠᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

$\red\checkmark\:\bf\blue{The\:sum\:of\:sides\:of\:the\:triangle\:=\:Perimeter\:of\:the\:triangle\:}$

$\bf{:\implies\:\dfrac{X}{3}\:+\:\dfrac{X}{4}\:+\:\dfrac{X}{5}\:=\:94\:}$

$\rm{:\implies\:\dfrac{20X\:+\:15X\:+\:12X}{60}\:=\:94\:}$

$\rm{:\implies\:47X\:=\:94\times{60}\:}$

$\rm{:\implies\:X\:=\:\dfrac{5640}{47}\:}$

$\bf\green{:\implies\:X\:=\:120\:cm\:}$

☯︎ Hᴇɴᴄᴇ, ᴛʜᴇ sɪᴅᴇs ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ᴀʀᴇ,

• $\bf{\dfrac{X}{3}\:=\:\dfrac{120}{3}\:=\:\pink{40\:cm}}$

• $\bf{\dfrac{X}{4}\:=\:\dfrac{120}{4}\:=\:\pink{30\:cm}}$

• $\bf{\dfrac{X}{5}\:=\:\dfrac{120}{5}\:=\:\pink{24\:cm}}$

$\huge\red\therefore$ Tʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ sᴍᴀʟʟᴇsᴛ sɪᴢᴇ ᴏғ ᴛʜᴇ ᴛʀɪᴀɴɢʟᴇ ɪs "24 ᴄm" .