Question

Polly Petals runs a small business creating flower gardens for people in her community. As spring approaches, the following customers have provided the dimensions of different flower gardens each would like to have created. • Rose Bush has a rectangular space with lengths of 3x + 1 and 2x +7. • Iris Orchid has a rectangular space with lengths 4x +2 and × + 5. • Sonny Flower has a square space with lengths of 4x + 2. a. Sketch the shape of each design to represent the space available for the flower gardens of each customer (label the lengths). Determine the area of space available for each customer

Answer 1

Here are the shapes and dimensions of each garden space:

Rose Bush: rectangular, 3x + 1 and 2x + 7

Iris Orchid: rectangular, 4x + 2 and x + 5

Sonny Flower: square, 4x + 2

To find the area of each garden space, you will need to use the formula for the area of a rectangle (length x width) or the area of a square (side length x side length). Here is how you would find the area of each space:

Rose Bush: (3x + 1) * (2x + 7) = 6x^2 + 7x + 2x + 7 = 6x^2 + 9x + 7

Iris Orchid: (4x + 2) * (x + 5) = 4x^2 + 9x + 2x + 10 = 4x^2 + 11x + 10

Sonny Flower: (4x + 2) * (4x + 2) = 16x^2 + 32x + 16x + 4 = 16x^2 + 48x + 4

Therefore, the area of the garden space for Rose Bush is 6x^2 + 9x + 7, the area of the garden space for Iris Orchid is 4x^2 + 11x + 10, and the area of the garden space for Sonny Flower is 16x^2 + 48x + 4.