Question

In a triangle the longest side is double the shortest side and the third side is 3 cm less than the longest side if the perimeter of the triangle is 72 cm find the sides of triangle

Answer 1

Let the shortest side of the triangle be x

And the longest side of the triangle be 2x

Given,

The third side is 3cm less than than the longest side. I.e. 2x - 3

We know,

Perimeter of a triangle = Sum of all its sides.

=> 72 = x + 2x + ( 2x - 3 )

=> 72 = 3x + 2x - 3

=> 72 + 3 = 5x

=> 75 = 5x

=> 75 / 5 = x

=> 15 = x

Therefore,

The shortest side of the triangle is 15 cm

The longest side of the triangle is ( 2 × 15 ) cm = 30cm

The third side of the triangle is ( 30 - 3 ) cm = 27 cm

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Answer 2

$\mathbb{\huge{\fbox{\red{Question:-}}}}$

In a triangle the longest side is double the shortest side and the third side is 3 cm less than the longest side if the perimeter of the triangle is 72 cm . Find the sides of triangle.

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

✏ The sides of triangle are :- 15 , 30 & 27 cm .

$\mathcal{\huge{\fbox{\purple{Solution:-}}}}$

Given :-

• The longest side of a Δ is double the shortest side

• The third side of a Δ is 3 cm less than the longest side

• The perimeter of the triangle is 72 cm

To Find :-

• The sides of triangle.

Calculation :-

Let us consider,

• The shortest side be x

• The longest side of the triangle be 2x

According to the question,

The third side is 3cm less than than the longest side.

=> ( 2x - 3 )

The Perimeter of a triangle = Sum of all its sides of a triangle.

↗ 72 = x + 2x + ( 2x - 3 )

↗ 72 = 3x + 2x - 3

↗ 72 + 3 = 3x + 2x

↗ 72 + 3 = 5x

↗ 75 = 5x

↗ 75/ 5 = x

▶ x = 15

◼ Hence, the shortest side of the triangle is 15 cm .

◼ The longest side of the triangle = 2x = ( 2 × 15 ) cm

= 30 cm.

◼ The third side of the triangle is ( 30 - 3 ) cm = 27 cm.

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$\mathcal{\huge{\fbox{\pink{Verification:-}}}}$

The Perimeter of a triangle = Sum of all its sides of a triangle.

➡ 72 = 15 + 30 + 27

➡ 72 = 45 + 27

➡ 72 = 72

Hence, L.H.S = R.H.S.

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