Question

If the sides of a parallelogram are increased to twice its original lengths, how much will the perimeter of the new parallelogram increase? ​

Answer 1

The perimeter is increased by twice to the original perimeter

Step-by-step explanation:

Given:-

the sides of a parallelogram are increased to twice its original lengths.

To find:-

How much will the perimeter of the new parallelogram increase?

Solution:-

Let the side of the Parallelogram be X units

Since opposite sides are equal then two sides are X and X units

and another side be Y units then the other two sides are Y and Y units

The four sides are X,X,Y,Y units

The perimeter of the paralellogram=P1

X+X+Y+Y

=>P1=2X+2Y units

=>P=2(X+Y) units.......(1)

If the all sides are increased twice then they becomes

2X,2X,2Y,2Y units

Perimeter=P2=2X+2X+2Y+2Y

=>P2=4X+4Y

=>P2=2[2(X+Y)] units

Answer:-

Perimeter is increased by twice to the previous perimeter of the Parallelogram

Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➙ Perimeter increased twice from the original parallelogram.

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

Given condition,

If the side of a parallelogram is increased by 2× it's original lengths how much the perimeter will increase.

Solution :

Here, we know that a parallelogram has equal opposite side. *[follow the attachment]*

Step 1 :

Considering the dimensions of the parallelogram :

• length = 'x' units.
• breadth = 'y' units.

Perimeter of a parallelogram is given by :

→ 2(l + b)

→ 2(x + y) units.

• Taking the perimeter of the parallelogram as $\sf {P}_{1}$

Step 2 :

Dimensions of the parallelogram increases twice the original :

So,

• length = '2x'
• breadth = '2y'

Perimeter of the parallelogram :

→ 2(l + b)

→ 2(2x + 2y)

→ 2*2(x + y)

→ 4(x + y) units.

• Taking $\sf {P}_{2}$ as the perimeter after increasing twice its original dimensions.

Step 3 :

Finding the perimeter increased :

$\sf \to \frac{{P}_{2}}{P_1}$

$\sf \to \frac{4(x + y) }{2(x + y) }$

$\sf \to {2units.}$

∴ Perimeter is increased twice from the original parallelogram.