Question

The perimeter of a triangle is 72 cm, and the
length of the sides are in the ratio 2 : 3: 4.
Find the lengths of the three sides in cm.
(A) 34, 24, 18
(B) 2, 3, 4
(C) 16, 24, 32
(D) None of these
​

Answer 1

Option c) 16, 24 & 32.

Question states that the perimeter of a given triangle is 72 cm and the length of the sides are in the ratio of 2 : 3 : 4. & we're asked to calculate all the three sides of the triangle$.$

Let's say, that the sides of the triangle be 2x, 3x and 4x respectively.

As we know that,

• Perimeter is sum of all the three sides of a triangle i.e. ( P ) = a + b + c. & Perimeter of the triangle is given which is 72 cm. Therefore:

★⠀Perimeter = a + b + c ★

↠⠀⠀2x + 3x + 4x = 72

↠⠀⠀9x = 72

↠⠀⠀x = 72⁄9

↠⠀⠀x = 8

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Therefore,

• 2x = 2(8) = 16 cm
• 3x = 3(8) = 24 cm
• 4x = 4(8) = 32 cm

⠀

❝ Hence, the sides of the triangle are Option c ) 16 cm, 24 cm & 32 cm. ❞

Answer 2

Answer:

16,24,32 OPTION (C)

Step-by-step explanation:

Let be the length of a side is 'x'

The ratios of the triangle = 2:3:4

The perimeter of triangle is 72 m.

The perimeter of the triangle (formula ) is AB+BC+CA

first side = 2× x =2x

second side = 3× x =3x

third side = 4× x =4x

According to the sum,

2x+3x+4x=72

9x =72

therefore, x = 72/9=8

first side = 2x = 2×8 = 16

second side = 3x = 3×8 = 24

third side =4x = 4×8 = 32

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