Question

The length of a rectangle is represented by x2 + 3x + 2, and the width is represented by 4x.

PART A:

Express the perimeter of the rectangle as a trinomial.

PART B:

Express the area of the rectangle as a trinomial.

Answer 1

A: Perimeter = 2*length + 2*width = 2x^2 + 14x + 4

B: Area = length*width = 4x^3 + 12x^2 + 8x

Answer 2

Perimeter of rectangle is 2x² + 14x + 4 and area of rectangle is 4x³ + 12x² + 8x.

What is Perimeter of rectangle?

The perimeter of a rectangle is defined as the sum of all the sides of a rectangle.

Here, given dimensions;

length of rectangle = x² + 3x + 2

width of rectangle = 4x

Here, we know that;

Perimeter of rectangle = 2 (l +w)

                                      = 2 (x² + 3x + 2 + 4x)

                                      = 2 (x² + 7x + 2)

                                      = 2x² + 14x + 4

Area of rectangle = length X width

                              = (x² + 3x + 2) X (4x)

                              = 4x³ + 12x² + 8x

Thus, Perimeter of rectangle is 2x² + 14x + 4 and area of rectangle is 4x³ + 12x² + 8x.

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