Calculate X in the Parallelogram: Step-by-Step to Find Height BE

Question

The area of the parallelogram below is 56.

BE is its height.

Calculate x.

00:00 Find X

00:03 In a parallelogram with equal opposite sides

00:12 We'll use the formula for calculating the area of a parallelogram (side times height)

00:20 We'll substitute the side values according to the given data

00:28 We'll substitute the area value according to the given data and solve for X

00:39 We'll use the shortened multiplication formulas to expand the brackets

00:54 Calculate 5 squared

01:03 Isolate X

01:14 Extract the root to find possible solutions for X

01:18 And this is the solution to the question

To solve this problem, we'll calculate $x$ using the provided expressions for the base and height of the parallelogram.

Given the area of the parallelogram:

$A = (\text{base}) \times (\text{height})$

In our case, the base is $x + 5$ , and the height is $x - 5$ . Therefore, we have:

$(x + 5)(x - 5) = 56$

Recognizing this as a difference of squares, we write:

$x^2 - 25 = 56$

Add 25 to both sides to isolate $x^2$ :

$x^2 = 81$

Take the square root of both sides:

$x = \pm 9$

Since both dimensions of a parallelogram must be positive in practical applications, we take $x = 9$ .

Therefore, the correct solution is $x = 9$ .

$9$