Parallelogram Side Length: Finding Missing Side Given 9cm and 30cm Perimeter

Video Solution

Solution Steps

00:00 Find AC

00:03 Opposite sides are equal in parallelograms

00:16 They are also a pair of opposite sides therefore equal

00:20 The perimeter of the parallelogram equals the sum of its sides

00:38 Let's substitute appropriate values and solve for BD

00:54 Group the numbers into one factor, and BD into one factor

01:04 Isolate BD

01:20 This is the length of BD

01:33 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

Let's work through each step:

Step 1: We are given that the perimeter of the parallelogram is 30 cm and one side $AB = 9$ cm. We need to find the other side, $b$ .

Step 2: The perimeter formula for a parallelogram is $P = 2(a + b)$ , where $a = 9$ cm and the perimeter $P = 30$ cm.

Step 3: Substitute the known values into the formula:

$30 = 2(9 + b)$

Divide both sides by 2 to simplify:

$15 = 9 + b$

Subtract 9 from both sides to solve for $b$ :

$b = 15 - 9$
$b = 6$

Therefore, the length of the other side is $\text{6 cm}$ .

Thus, the solution to the problem is $b = 6$ cm.