Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Question 12Sophia wants to plant a garden that will be in the shape of arectangle. She was given 80 feet of fencing to enclose the garden(perimeter). She wants the length to be 10 feet more than twicethe width. What are the dimensions, in feet, of Sophia's garden ifshe uses all 80 feet of fencing?

Sagot :

EXPLANATION

Let's see the facts:

Sophia's garden shape: rectangular

The perimeter of the garden = 80 ft (conditional)

Length = 10+2Width ---> l = 10+2w (conditional)

As we can see, there are two variables and two equations, so we must solve this system of equations:

(1) p = 2 (w+l) = 80 (Perimeter Formula)

(2) l = 10 + 2w (Conditional)

Now, we can solve (1) equation and replace in (2):

80 = 2w + 2l (Isolating w)

80 - 2l = 2w (Dividing both sides by 2)

40 - l = w

Now, replacing in (2):

l = 10 + 2(40-l) (Applying distributive property)

l = 10 + 80 - 2l (Adding +2l to both sides and simplifying)

3l = 90 (Dividing both sides by 3)

l = 30

Now, we have l=30, so with this variable can calculate w in this way:

w = 40 - l = 40 - 30 = 10

w = 10

Now we have the dimensions: Width=10ft and Length= 30ft

[ANSWER] The dimensions are: Width=10 feet and Length= 30 feet

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.