Calculate Side CD in a Parallelogram with Perimeter 15cm and AB = 5cm

A parallelogram has a perimeter of 15 cm.

AB = 5 cm

Calculate side CD.

Video Solution

Solution Steps

00:00 Find AC

00:03 Opposite sides are equal in parallelograms

00:17 They are also a pair of opposite sides therefore equal

00:22 The perimeter of the parallelogram equals the sum of its sides

00:37 We'll substitute appropriate values and solve for BD

00:51 We'll group the numbers into one factor, and BD into one factor

01:00 We'll isolate BD

01:11 This is the length of BD

01:19 And this is the solution to the question

Step-by-Step Solution

To solve for the side $CD$ in the given parallelogram:

Step 1: Identify the given information: the perimeter $P = 15 \, \text{cm}$ and side $AB = 5 \, \text{cm}$ .
Step 2: Apply the perimeter formula for a parallelogram $P = 2(a + b)$ .
Step 3: Relate the perimeter to the given sides. Set $a = AB = 5 \, \text{cm}$ and $b = CD$ .

Substituting into the formula, the equation is:

$15 = 2(5 + CD)$ .

Simplify and solve for $CD$ :

$15 = 10 + 2CD$ .

Subtract 10 from both sides:

$5 = 2CD$ .

Divide both sides by 2:

$CD = \frac{5}{2} = 2.5 \, \text{cm}$ .

Therefore, the length of side $CD$ is $2.5 \, \text{cm}$ .

By calculating, the correct answer choice is: $2.5 \, \text{cm}$ .