Question

the three sides of a triangle are consecutive integers and their perimeter is 72 cm. Find the measure of each side of a triangle.
plz answer it fast and correctly because tomorrow is my test ​

Answer 1

✬ Sides = 23 , 24 , 25 cm ✬

Step-by-step explanation:

Given:

• Measure of three sides of a triangle are consecutive integers.
• Perimeter of triangle is 72 cm.

To Find:

• What is measure of each side of triangle ?

Solution: Let the first integer be x , second be x + 1 , third be x + 2. Therefore,

➟ First side = x cm

➟ Second side = (x + 1) cm

➟ Third sides = (x + 2) cm

As we know that

★ Perimeter of ∆ = Sum of all sides ★

A/q

• Perimeter is 72 cm

$\implies{\rm }$ x + x + 1 + x + 2 = 72

$\implies{\rm }$ 3x + 3 = 72

$\implies{\rm }$ 3x = 72 – 3

$\implies{\rm }$ 3x = 69

$\implies{\rm }$ x = 69/3

$\implies{\rm }$ x = 23

Hence, Sides of triangle are

➭ First side = x = 23 cm

➭ Second side = x + 1 = 23 + 1 = 24 cm

➭ Third side = x + 2 = 23 + 2 = 25 cm

__________________

★ Verification ★

=> 23 + 24 + 25 = 72

=> 47 + 25 = 72

=> 72 = 72

$\large\boxed{\texttt{Verified}}$

Answer 2

$\mathfrak{\huge{\underline{\underline{\red{Question\:?}}}}}$

✨ The three sides of a triangle are consecutive integers and their perimeter is 72 cm. Find the measure of each side of a triangle.

$\mathcal{\huge{\underline{\underline{\green{AnSwEr:-}}}}}$

✒ The measure of each side of triangle are 23 , 24 & 25 cm .

$\mathcal{\huge{\underline{\underline{\pink{Solution:-}}}}}$

Given :-

• The measure of three sides of a triangle are consecutive integers.

• The Perimeter of triangle is 72 cm.

To Find :-

The measure of each side of triangle .

Calculation :-

Let the first integer be x , second be x + 1 , third be x + 2. {Given, the measure of three sides of a triangle are consecutive integers.}

▶ I side = x cm

▶ II side = (x + 1) cm

▶ III sides = (x + 2) cm

✏ The Perimeter of ∆ = ( a + b + c )

According to the question ,

⭐ The Perimeter of triangle is 72 cm.{Given}

⟿ x + (x + 1) + (x + 2) = 72

⟿ x + x + x + 1 + 2 = 72

⟿ 3x + 3 = 72

⟿ 3x = 72 – 3

⟿ 3x = 69

⟿ x = 69/3

⟿ x = 23

Therefore, The Sides of triangle are ,

I side => x = 23 cm

II side => (x + 1) = 23 + 1 = 24 cm

III side => (x + 2) = 23 + 2 = 25 cm

➡ So, the three sides of triangle are 23 , 24 & 25 cm .

____________________________________

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▶R.H.S

= 23 + 24 + 25

= 47 + 25

➡ 72

▶L.H.S

= 72

✳ The Perimeter of ∆ = ( a + b + c )

↗ 72 = 72

Hence, Verified ☑

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