Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

A garden measuring 15 meters by 20 meters is to have a pedestrian pathway installed
all around it, increasing the area to 336 square meters.
a. Write an expression to represent the area of the total garden including the
pathway.

b. What will be the width of the pathway?

Sagot :

MrRoyal

The area of the garden is the amount of space on the garden.

  • The area of the total garden is (x + 15)(x + 20)
  • The width of the pathway is 1 meter

The expression of the area

The dimensions of the garden is given as:

15 meters by 20 meters

Let the width of the pedestrian pathway be x.

So, the area of the total garden is:

[tex]Area=(x + 15)(x + 20)[/tex]

The width of the pathway

In (a), we have:

[tex]Area=(x + 15)(x + 20)[/tex]

The total area is given as: 336.

So, we have:

[tex](x + 15)(x + 20) = 336[/tex]

Expand

[tex]x^2 + 35x + 300 = 336[/tex]

Collect like terms

[tex]x^2 + 35x + 300 - 336 = 0[/tex]

Evaluate

[tex]x^2 + 35x - 36 = 0[/tex]

Expand

[tex]x^2 + 36x -x - 36 = 0[/tex]

Factorize

[tex]x(x + 36) -1(x +36) = 0[/tex]

Factor out x + 36

[tex](x + 36)(x -1) = 0[/tex]

Solve for x

x = -36 or x =1

The width cannot be negative.

Hence, the width of the pathway is 1 meter

Read more about areas at:

https://brainly.com/question/24487155

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.