Calculate Parallelogram Side Length CD Given 45cm Perimeter and AB=15cm

A parallelogram has a perimeter of 45 cm

AB = 15 cm

Calculate side CD.

Video Solution

Solution Steps

00:00 Find AC

00:03 Opposite sides are equal in a parallelogram

00:14 They are also a pair of opposite sides therefore equal

00:19 The perimeter of the parallelogram equals the sum of its sides

00:30 Let's substitute appropriate values and solve for AC

00:45 Group the numbers to one factor, and AC to one factor

00:53 Isolate AC

01:09 This is the length of AC

01:14 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will calculate side $CD$ using the perimeter formula of a parallelogram:

The perimeter formula of a parallelogram is $P = 2 \times (AB + CD)$ .
Given $P = 45$ cm and $AB = 15$ cm, substitute these values into the equation: $45 = 2 \times (15 + CD)$ .
Simplify the expression: $45 = 30 + 2 \times CD$ .
Rearrange the equation to solve for $CD$ : $2 \times CD = 45 - 30$ .
This simplifies to: $2 \times CD = 15$ .
Divide both sides by $2$ to find $CD$ : $CD = \frac{15}{2}$ .
Thus, $CD = 7.5$ cm.

Therefore, the length of side $CD$ is $7.5$ cm.