Question

Part A: The area of a square is (16x2 + 24x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points)

Part B: The area of a rectangle is (4x2 − 49y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Answer 1

The dimensions of the rectangle are  (2x + 7y) and (2x - 7y)

Area of a square

The formula for calculating the area of a square is expressed as:

A = L^2

Given the area of a square expressed as 16x^2 + 24x + 9

Factorize 16x^2 + 24x + 9

16x^2 + 24x + 9

=  16x^2 + 12x + 12x + 9

= 4x(4x+3) + 3(4x+3)

= (4x+3)^2

Hence the lngth of each side of the square is 4x+3

For the funciton 4x^2 − 49y^2

On factoring completely

4x^2 − 49y^2

= (2x)^2 - (7y)^2

= (2x + 7y)(2x - 7y)

Hence the dimension of the rectangle are  (2x + 7y) and (2x - 7y)

Learn more on area of a square heere; https://brainly.com/question/25092270