The area of a rectangle is 10 cm^2. One side of the rectangle is x cm. Express the perimeter of the rectangle in terms of x.
A = Area
P = Perimeter
One side is x.
Mark the other side with y.
A = x ∙ y
The area of a rectangle is 10 cm² so:
x ∙ y = 10
Divide both sides by x
y = 10 / x
P = 2 ( x + y )
P = 2 ( x + 10 / x )
P = 2 ( x ∙ x / x + 10 / x )
P = 2 ( x² / x + 10 / x )
P = 2 ( x² + 10 ) / x
To find the perimeter of a rectangle, we need to know the lengths of both sides of the rectangle. However, in this case, only one side is given as x cm. Since the area of the rectangle is given as 10 cm^2, we can use this information to find the length of the other side.
The formula to calculate the area of a rectangle is: Area = length × width.
Given that the area is 10 cm^2 and one side is x cm, we can set up the equation:
10 = x × width
To solve for the width, we divide both sides of the equation by x:
10 / x = width
So, the width of the rectangle is 10/x cm.
Now that we have both the length and width of the rectangle, we can calculate the perimeter.
The formula for the perimeter of a rectangle is: Perimeter = 2 × (length + width)
Substituting the values we found:
Perimeter = 2 × (x + 10/x)
So, the perimeter of the rectangle, expressed in terms of x, is 2(x + 10/x) cm.