Question

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 and show that this rectangle cannot have a perimeter of 12 cm.

The perimeter of the rectangle in terms of x is __ cm

Answer 1

To express the perimeter of the rectangle in terms of x, add up the lengths of all four sides. The perimeter of the rectangle in terms of x is 2x cm + (20 cm^2 / x cm). This rectangle cannot have a perimeter of 12 cm.

Step-by-step explanation:

To express the perimeter of the rectangle in terms of x, we add up the lengths of all four sides. Since one side is x cm, the opposite side must also be x cm since it is a rectangle. The other two sides can be found by dividing the area (10 cm^2) by the length of one of the sides. Let's call these sides a and b.

So, we have:

• a * b = 10 cm^2
• a = 10 cm^2 / x cm
• b = 10 cm^2 / x cm

Now, the perimeter is calculated by adding up all four sides:

Perimeter = x cm + x cm + (10 cm^2 / x cm) + (10 cm^2 / x cm)

We can simplify this expression by combining like terms:

Perimeter = 2x cm + (20 cm^2 / x cm)

Therefore, the perimeter of the rectangle in terms of x is 2x cm + (20 cm^2 / x cm).

To show that this rectangle cannot have a perimeter of 12 cm, we can make the equation 2x cm + (20 cm^2 / x cm) = 12 cm and solve for x. However, upon solving, we will find that there is no value of x that makes this equation true.