Exploring Area & Perimeter with Polynomials in 8th Grade

A rectangular garden has a length of (2x + 3) meters and a width of (x + 1) meters. What is the area of the garden in square meters?

• x^2 + 3x + 2

• 2x^2 + 6x + 3

• 2x^2 + 4x + 1

• 2x^2 + 5x + 3

The perimeter of a rectangular pool is represented by the expression (2x + 10) meters. If the length is (x + 5) meters, what is the width of the pool?

• 0 meters

• 5 meters

• 10 meters

• x meters

A rectangular field has a length of (3x - 2) meters and a width of (x + 4) meters. Calculate the perimeter of the field.

• 6x + 8 meters

• 10x - 4 meters

• 8x + 4 meters

• 4x + 6 meters

A square park has a side length of (x + 2) meters. Write a polynomial expression for the area of the park and evaluate it for x = 3.

• 15 square meters

• 30 square meters

• 20 square meters

• 25 square meters

The area of a rectangular classroom is given by the polynomial expression (x^2 + 5x + 6) square meters. If the width is (x + 2) meters, find the length of the classroom.

• x + 3

• x + 1

• x + 5

• x + 4

A rectangular box has a length of (x + 3) cm, a width of (2x - 1) cm, and a height of (x + 4) cm. What is the volume of the box in cubic centimeters?

• x^3 + 5x^2 + 8x + 2

• 4x^3 + 12x^2 + 20x - 8

• 2x^3 + 13x^2 + 17x - 12

• 3x^3 + 10x^2 + 15x - 5

The area of a triangular garden is represented by the expression (1/2 * base * height). If the base is (x + 5) meters and the height is (2x - 3) meters, find the area in terms of x.

• x^2 + (7/2)x - (15/2)

• (1/2 * (x + 5) * (2x + 5))

• (1/2 * (x - 5) * (2x - 3))

• (1/2 * (x + 5) * (2x + 3))

A rectangular plot of land has a length of (4x + 1) meters and a width of (2x - 3) meters. What is the expression for the perimeter of the plot?

• 10x - 6

• 8x + 2

• 14x - 8

• 12x - 4

A rectangular room has a length of (x + 6) feet and a width of (3x - 2) feet. Calculate the area of the room in square feet.

• 2x^2 + 10x - 8

• 3x^2 + 16x - 12

• 4x^2 + 12x - 20

• 3x^2 + 8x - 5

The perimeter of a rectangular fence is (6x + 20) meters. If the length is (2x + 5) meters, find the width of the fence.

• 3x + 5

• x + 10

• x + 5

• 2x + 10