Question

ABCD is a parallelogram with perimeter 40. Find the values of x and y.

Answer 1

Explanation:

Values are X = 4 and Y = 5.

Given:

A figure of ||gm ABCD and side lengths are given.

The perimeter of ||gm is 40 cm.

To find:

Find the value of x and y.

Solution:

Concept/ formula to be used:

According to the property of ||gm, its opposite sides are equal.

Perimeter: Sum of all sides.

Step 1:

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

We know that

AB= DC

and AD= BC= 2x

So,

3x=2y+2

or

3x−2y=2...eq1

Step 2:

Write an equation for the perimeter.

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

or

7x+2y=38...eq2

Step 3:

Add eq1 and eq2.

3x−2y=2

7x+2y=38

−−−−−−

10x=40

or

x=4

put the value of x in eq1.

3(4)−2y=2

or

−2y=2−12

or

−2y=−10

or

y=5

Thus,

Value of x and y are 4 and 5 respectively.