Parallelogram Side Length: Finding CD When Perimeter is 70cm and AB=20cm

A parallelogram has a perimeter of 70 cm.

AB = 20 cm

Calculate side CD.

Video Solution

Solution Steps

00:00 Find AC

00:03 Opposite sides are equal in a parallelogram

00:13 They are also a pair of opposite sides therefore equal

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

00:29 Let's substitute appropriate values and solve for BD

00:45 Group the numbers into one factor, and BD into one factor

00:54 Isolate BD

01:07 This is the length of BD

01:14 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll use the formula for the perimeter of a parallelogram:

Step 1: Identify the given information:
The perimeter $P$ is 70 cm, and the side $AB = 20$ cm.
Step 2: Apply the perimeter formula:
The formula for the perimeter of a parallelogram is $P = 2(a + b)$ , where $a$ and $b$ are the lengths of adjacent sides.
Step 3: Set up the equation:
Let $CD = x$ . Then, the equation becomes: $70 = 2(20 + x)$
Step 4: Solve for $x$ :
Divide both sides by 2: $35 = 20 + x$ Subtract 20 from both sides: $x = 15$

Therefore, the length of side CD is $15$ cm.