Calculate Parallelogram Side Length: Given 25cm Perimeter and 8cm Side

Given the parallelogram whose perimeter is equal to 25 cm and AB=8 cm:

Calculate the other side.

Video Solution

Solution Steps

00:00 Find AC

00:03 Opposite sides are equal in a parallelogram

00:18 They are also a pair of opposite sides, therefore equal

00:24 The perimeter of the parallelogram equals the sum of its sides

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

00:54 Let's group the numbers to one factor, and BD to one factor

01:02 Let's isolate BD

01:17 This is the length of BD

01:28 And this is the solution to the problem

Step-by-Step Solution

Let's solve this problem step-by-step:

Step 1: Understand the problem
We are given the perimeter of the parallelogram as 25 cm and one side $AB$ as 8 cm. We need to calculate the length of the other side of the parallelogram, $BC$ .
Step 2: Recall the formula for the perimeter of a parallelogram
The perimeter $P$ of a parallelogram is given by:
$P = 2(a + b)$
Where $a$ and $b$ are lengths of adjacent sides.
Step 3: Apply the given information
We have $P = 25$ cm and one side $a = AB = 8$ cm. Substitute these into the formula:
$25 = 2(8 + b)$
Step 4: Solve for the unknown side $b$
First, divide both sides by 2:
$12.5 = 8 + b$
Subtract 8 from both sides:
$b = 12.5 - 8$
$b = 4.5$
Therefore, the length of the other side is $4.5$ cm.

Upon checking with the given choices, the correct answer is indeed 4.5.