Write an expression for the area of the shape. Write and simplify an expression for the perimeter of the shape. Calculate the area and perimeter of the shape for each valueof \( x \). h. \( x=7 \) i. \( x=2.5 \) j. \( x=15 \)

To find the area and perimeter of a given shape, you'll first need to establish an expression based on its dimensions, typically involving \( x \) if that's the variable used. For instance, if the shape is a rectangle where the length is \( 2x \) and the width is \( x + 3 \), the area \( A \) can be expressed as: \[ A = \text{Length} \times \text{Width} = (2x)(x + 3) = 2x^2 + 6x \] For perimeter \( P \), the formula is: \[ P = 2(\text{Length} + \text{Width}) = 2(2x + (x + 3)) = 2(3x + 3) = 6x + 6 \] Now, plug in the values of \( x \): For \( x = 7 \): Area: \[ A = 2(7)^2 + 6(7) = 2 \times 49 + 42 = 98 + 42 = 140 \] Perimeter: \[ P = 6(7) + 6 = 42 + 6 = 48 \] For \( x = 2.5 \): Area: \[ A = 2(2.5)^2 + 6(2.5) = 2 \times 6.25 + 15 = 12.5 + 15 = 27.5 \] Perimeter: \[ P = 6(2.5) + 6 = 15 + 6 = 21 \] For \( x = 15 \): Area: \[ A = 2(15)^2 + 6(15) = 2 \times 225 + 90 = 450 + 90 = 540 \] Perimeter: \[ P = 6(15) + 6 = 90 + 6 = 96 \] So, the area and perimeter calculations for different \( x \) values highlight how the shape expands as \( x \) increases!