Question

The adjacent sides of a parallelogram are in the ratio 4: 7. If its perimeter is 176 cm, find the sides of the parallelogram.​

Answer 1

Given :-

The adjacent sides of a parallelogram are in the ratio 4: 7. If its perimeter is 176 cm,

To Find :-

find the sides of the parallelogram.​

Solution :-

Let the adjacent side be 4x and 7x

Perimeter = 2(l + b)

176 = 2(4x + 7x)

176/2 = 4x + 7x

88 = 11x

88/11 = x

8 = x

Hence

Length = 7x = 7(8) = 56 cm

Breadth = 4x = 4(8) = 32 cm

Answer 2

Answer:

Sides are 32 cm, 56 cm, 32 cm, 56 cm

Step-by-step explanation:

Given:

• 2 adjacent sides of a parallelogram are in the ratio 4 : 7
• Perimeter = 176 cm

To find:

Sides of parallelogram = ?

Solution:

Let the 2 adjacent sides of parallelogram be 4x and 7x.

The opposite sides of a parallelogram are equal.

So, the 4 sides of the parallelogram are

→ 4x, 7x, 4x, 7x.

   Perimeter = Sum of all sides

⇒ 176 = 4x + 7x + 4x + 7x

⇒ 176 = 22x

⇒ x = 176 ÷ 22

⇒ x = 8

For finding sides:

Adjacent sides are 4x, 7x as considered earlier.

• 4x = 4(8) = 32 cm
• 7x = 7(8) = 56 cm

∴ Sides are 32 cm, 56 cm, 32 cm, 56 cm

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Second method (shortcut)

Perimeter of parallelogram = 2 (Sum of adjacent sides)

⇒ 176 = 2 (4x + 7x)

⇒ 176 = 2 (11x)

⇒ x = 8

Sides are 4x and 7x

Substituting x: sides = 4 × 8 and 7 × 8

⇒ Sides are 32 cm, 56 cm, 32 cm, 56 cm