Question

The length of a parallelogram is 2.5 m longer than its adjacent side. If the perimeter of the parallelogram
is 51 m, find the measure of all its sides.
​

Answer 1

Given :-

◉ The length of a parallelogram is 2.5 m longer than its adjacent side.

◉ Perimeter of the parallelogram is 51 m.

To Find :-

◉ Measure of all its sides

Solution :-

Let the side of the parallelogram be x then the adjacent side will be x + 2.5

We know, The opposite sides of a Parallelogram are equal and parallel.

So,

⇒ Perimeter = sum of all sides

⇒ (x) + (x) + (x + 2.5) + (x + 2.5) = 51

⇒ 4x + 5 = 51

⇒ 4x = 46

⇒ x = 23/2

⇒ x = 11.5

The four sides of the Parallelogram are x , x , x + 2.5 , x + 2.5

⇒ Sides are 11.5 m , 11.5 m, (11.5 + 2.5) m , (11.5 + 2.5)

Hence, The sides of the Parallelogram are 11.5 m, 11.5 m , 14 m , 14 m respectively.

Some Information :-

☛ Parallelogram is a quadrilateral enclosed by four lines. Properties of Parallelogram:

• Opposite sides are equal and parallel to each other.
• Adjacent angles sum up to 180°.
• Opposite angles are equal.
• Diagonal of a Parallelogram divides the Parallelogram into two triangles of equal area which are also congruent to each other.

Answer 2

★ QUESTION :

The length of a parallelogram is 2.5 m longer than its adjacent side. If the perimeter of the parallelogram is 51 m. Find the measure of all its sides.

GIVEN :

• The length of the parallelogram = 2.5 m

• The Perimeter of the parallelogram = 51 m

TO FIND :

• The measures of all its side = ?

STEP - BY - STEP EXPLAINATION :

Now, here let us consider the adjacent side of a parallelogram as x + 2.5 and side of a parallelogram as x

⟹ Perimeter of the parallelogram = sum of the all sides of the parallelogram

⟹ x + x + (x + 2.5) + (x + 2.5) = 51

⟹ 4x + 5 = 51

⟹ 4x = 51 - 5

⟹ 4x = 46

⟹ x = 23 / 2

⟹ x = 11.5

Now, as we know that there are four sides of the parallelogram,

The four sides of parallelogram we have obtained are (x) , (x) , (x + 2.5) , (x + 2.5)

And Let us considered the side as x

Sides of the parallelogram are as follows : 11.5x , 11.5x , (11.5 + 2.5) , (11.5 + 2.5)

→ 11.5x , 11.5x , 14x and 14x

➠ Therefore, the measures of all its four side are 11.5x , 11.5x, 14x, 14x