Question

ABCD is a parallelogram with perimeter 40cm find X and Y

Answer 1

Answer:

Step-by-step explanation:

First of all, AD=BC, so BC also is 2x.  

Secondly, AB=CD, so 3x=2y+2. If you solve for 2y, 2y=3x-2  

Thirdly, Perimeter = Sum of four sides

2x+3x+2x+2y+2 = 40  

Simplify:

7x+2y+2=40  

Substitute 2y=3x+2:

 

7x + 3x-2+2=40

10x=40

x=4  

2y=3x-2

2y=3*4-2

2y=10

y=5  

Answer 2

Values are $\bf x = 4$ and $\bf y = 5$.

Given:

• A figure of ||gm ABCD and side lengths are given.
• Perimeter of ||gm is 40 cm.

To find:

• Find the value of x and y.

Solution:

Concept/ formula to be used:

1. According to property of ||gm, it's opposite sides are equal.
2. Perimeter: Sum of all sides.

Step 1:

Mark the vertices of ||gm as shown in attachment.

We know that

AB= DC

and AD= BC= 2x

So,

$3x = 2y + 2$

or

$\bf 3x - 2y = 2...eq1$

Step 2:

Write equation for perimeter.

$2x + 3x + 2x + 2y + 2 = 40$

or

$\bf 7x + 2y = 38...eq2$

Step 3:

Add eq1 and eq2.

$3x - 2y = 2 \\ 7x + 2y = 38 \\ - - - - - - \\ 10x = 40$

or

$\bf x = 4$

put value of x in eq1.

$3(4) - 2y = 2$

or

$- 2y = 2 - 12$

or

$- 2y = - 10$

or

$\bf y = 5$

Thus,

Value of x and y are 4 and 5 respectively.

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