Calculate Parallelogram Side Length: AB = AE + 3cm with Area 32cm²

Question

AE is the height of the parallelogram ABCD.

AB is 3 cm longer than AE.

The area of ABCD is 32 cm².

Calculate the length of side AB.

00:00 Find AB

00:03 The formula for calculating the area of a parallelogram is height(AE) multiplied by side(AB)

00:10 The side length according to the given data

00:14 Let's solve for AE

00:18 Let's make sure to open the parentheses properly

00:22 And put 0 on the right side of the equation

00:28 These are the possible solutions for AE

00:43 The side cannot be a negative length

00:50 Therefore this is the solution for AE and we'll substitute it to find AB

00:55 And this is the solution to the question

Keep in mind that AB is 3 cm greater than AE, so we must pay attention to the data when we put the formula to calculate the parallelogram:

Height multiplied by the side of the height:

$AB\times AE=S$

We will mark AE with the letter a and therefore AB will be a+3:

$a\times(a+3)=32$

We open the parentheses:

$a^2+3a=32$

We use the trinomial/roots formula:

$a^2+3a-32=0$ $(a+8)(a-5)=0$

That means we have two options:

$a=-8,a=5$

Since it is not possible to place a negative side in the formula to calculate the area $a=5$

Now we can calculate the sides:

$AE=5$

$AB=5+3=8$

8 cm