Perimeter using a simplified expression

Front

What is the formula for the perimeter of a rectangle?

Back

The perimeter (P) of a rectangle is given by the formula P = 2(length + width).

Front

If the length of a rectangle is 3x and the width is 4, what is the perimeter?

Back

P = 2(3x + 4) = 6x + 8.

Front

What is the area of a rectangle?

Back

The area (A) of a rectangle is calculated using the formula A = length × width.

Front

If the length of a rectangle is 5x and the width is 2x, what is the area?

Back

A = 5x × 2x = 10x².

Front

How do you simplify the expression for the perimeter of a rectangle with length 2x + 3 and width x + 1?

Back

P = 2((2x + 3) + (x + 1)) = 2(3x + 4) = 6x + 8.

Front

What does it mean to express the perimeter in simplified form?

Back

Expressing the perimeter in simplified form means combining like terms and writing the expression in the simplest way possible.

Front

If a rectangle has a perimeter of 20 and the length is 6, what is the width?

Back

Using P = 2(length + width), we have 20 = 2(6 + width). Solving gives width = 4.

Front

What is the relationship between the area and perimeter of a rectangle?

Back

The area measures the space inside the rectangle, while the perimeter measures the distance around it.

Front

If the perimeter of a rectangle is given as 16x + 20, what is the simplified expression for the width if the length is 4x + 5?

Back

Using P = 2(length + width), we can find width = (16x + 20)/2 - (4x + 5) = 4x + 5.

Front

What is the significance of the coefficients in the expressions for area and perimeter?

Back

Coefficients represent the dimensions of the rectangle; they indicate how the area and perimeter change with varying lengths and widths.