Question

The sides of a triangle are in the ratio 3:5:7 and its perimeter is 45 cm. What are the
lengths of the sides?
​

Answer 1

The length of the sides be 9cm, 15cm, 21cm

Step-by-step explanation:

$\underline \frak{Given} :$

• Triangle are in the ratio 3 : 5 : 7

• Perimeter of triangle = 45cm

$\underline \frak{T o \: find }:$

• The length of the sides ?

$\underline{ \underline \frak{ \green{ \underline{ \underline{Solution : }}}}}$

Let the sides of the triangle be

• 1st side = 3x

• 2nd side = 5x

• 3rd side = 7x

$\red{ \frak{ According \: to \: question }}$

$\longrightarrow\sf \: 3x + 5x + 7x = 45$

$\sf \longrightarrow15x = 45$

$\sf \: \longrightarrow \: x = \frac{ \cancel{45}}{ \cancel{15}}$

$\qquad{ } \boxed{ \frak{ \longrightarrow \: x = 3}}$

Hence,

$\tt {1}^{st} \: side \: 3x\\ \tt \longrightarrow\: 3 \times 3 \\ \tt \longrightarrow \frak{9 \: cm}$

$\tt {2}^{nd} \: side \: 5x \\ \tt \: \longrightarrow5 \times 3 \\ \tt \longrightarrow \frak{15 \: cm}$

$\tt {3}^{rd} \: side \:7x \\ \longrightarrow \tt7 \times 3 \\ \tt \longrightarrow \frak{21 \: cm}$

Therefore the length of the sides be

• 1st side = 9cm
• 2nd side = 15cm
• 3rd side = 21cm

Answer 2

perimeter of the triangle =60cm

3x+5x+7x=60

⇒15x=60

⇒x=60/15

⇒x=4

3x=3×4=12cm

5x=5×4=20cm

7x=7×4=28cm

S= 1/2(a+b+c)

= 1/2×60

=30

Area = 30(30−12)(30−20)(30−28)

= 30×8×10×2

= 60×180

= 10800

= 3600×3

=60 ÷ 3cm ²

Area of triangle =60 ÷3cm²

Hope it helps ❤️