Answer: 20 cm
The area [tex]A_{parallelogram}[/tex] of a parallelogram is given by the following formula:
[tex]A_{parallelogram}=wh=24{cm}^{2}[/tex] (1)
Where [tex]w[/tex] is the width and [tex]h[/tex] is the height of the parallelogram.
Now, let's call the point of intersection of the diagonals c. We know the distances between c and the sides are 2 cm and 3 cm, respectively, as shown in the figure attached.
From this we are able to know that the distance between c and one of the sides is the half of the width, and the distance between c and the other side is the half of the height.
This means the width of the parallelogram is:
[tex]w=6cm[/tex] (2)
And its height is:
[tex]h=4cm[/tex] (3)
We can prove this with the formula of the area of the parallelogram (1):
[tex]A_{parallelogram}=(6cm)(4cm)=24{cm}^{2}[/tex]
Now, the perimeter of a parallelogram is:
[tex]P_{parallelogram}=2(w+h)[/tex] (4)
Substituting the values of [tex]w[/tex] and [tex]h[/tex] in (4):
[tex]P_{parallelogram}=2(6cm+4cm)[/tex]
We finally get the perimeter:
[tex]P_{parallelogram}=20cm[/tex]
The perimeter of the parallelogram is 20 cm
From the given question,
The formula to determine the area of a parallelogram is base multiply by the height, which can be expressed as:
A = base x height
Recall that the distance between the point of intersection of the diagonals and the opposite sides are same
Therefore, you have:
h₁ = 2 + 2 = 4 cm
h₂ = 3 + 3 = 6 cm
If you substitute the value of h₁ into the formula, you have:
24 = b₁ x 4
b₁ = 24/4
b₁ = 6
Therefore, the measure of one side is 6 cm
To determine the measure of the second side, then you have to substitute the value of h₂ into the formula, you have:
24 = b₂ x 6
b₂ = 24/6
b₂ = 4 cm
Now, to determine the perimeter of the parallelogram, then you have:
P = 2 (b₁ + b₂)
P = 2 (6 + 4)
P = 2 (10)
P = 20 cm.
The formulas used are:
A = base x height
P = 2 (b₁ + b₂)
Therefore, the perimeter of the parallelogram is 20 cm
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