algebra 1 help please, explain all answers

Question

The movie, Hidden Figures tells the story of how 3 african american women Katherine G johnson, Dorothy Vaughan, and mary jackson, teamed up to solve nasa's mathematical equations during the sace race in the sixties . some documents have been discovered at nasa that include graphs tables and calculations that may have belonged to these ladies your job is to organize these documents into a collection that can be displayed at the smithsonian national museum of african american history & culture in washington Dc

The floor of the room where the documents will be displayed is rectangular in shape. the length of the floor is four times the width the floor area is 144 square feet. write and solve a quadratic equation to find the length of the display floor. show the steps you used to solve the problem and write your answer in a complete sentence

Part A Write the equation used to find the length of the of the display floor. *

Part B Determine the length and the width of the display floor and write your answer in a complete sentence. *

Answer 1

Area of a rectangle: Area = length * width

In this case:

Length: l = 4w

Area: A = 144

So, the area is:

144 = 4w * w

144 = 4w²

Base on the Area formula, we determine the quadratic equation to solve the problem:

0 = 4w² - 144

4w² - 144 = 0

Quadratic Equation:

(2w)² - 12² = 0

Difference of squares:

(2w + 12) (2w - 12) = 0

To find the values of w, we must solve: 2w+12=0 and 2w-12=0

2w + 12 = 0

2w = -12

w = -12/2

w = -6 Since w represents the wide of the rectangle, it cannot be a negative number so w=-6 is not a possible solution.

2w - 12 = 0

2w = 12

w = 12/2

w = 6

Length:

l = 4w

l = 4(6)

l = 24

The length of the floor is 24 feet, and the width is 6 feet.