Question

Ben fenced his backyard using 350 feet of fencing. The width of his yard is 12 feet less than twice the length. Write an equation that can be used to determine the dimensions of his yard and solve.

Answer 1

Hello @candygirl200 Do you mind if I help you today?

Answer 2

sure u could help

Answer 3

"The width of his yard is 12 feet less than twice the length."

w = 2l - 12

Where,
w = width
l = length

Answer 4

Going to assume that this is a rectangular backyard (as they usually are).

The formula for the perimeter of a rectangle can be written as,
P = 2l + 2w

Where P is the perimeter

Answer 5

Right now we have three variables. P, w, and l

In order to solve for a variable in any algebraic equation, we must have only ONE unknown.

"Ben fenced his backyard using 350 feet of fencing."

With this sentence we know that P = 350ft as a fence goes around the "perimeter"

Then with that information we start working some magic with our two equations that I showed.

w = 2l - 12

P = 2l + 2w

We will be using the second one as it expresses the dimensions of the yard in terms of the perimeter.

We can replace P with 350ft

350ft = 2l + 2w

We have w defined in our earlier equation, so we can do

\[350ft = 2l + 2(2l - 12) \]

Answer 6

Are you with me so far?

Answer 7

yes

Answer 8

\[350 = 2l + 2(2l - 12) \]

We solve for our unknown, the length

\[350 = 2l + 4l - 24\]

\[350 = 6l - 24\]

\[374 = 6l\]

\[l = \frac{ 187 }{ 3 }\]

Answer 9

Where do you think we go from here?

Answer 10

plug in to find w

Answer 11

Exactly. Which equation would we use?

Answer 12

the original one

Answer 13

We can use both P = 2l + 2w and w = 2l - 12, but it is easier to use the second one since it is already in terms of w.

\[w = 2l - 12\]

\[w = 2(\frac{ 187 }{ 3 }) - 12\]

\[w = \frac{ 374 }{ 3 } - 12\]

\[w = \frac{ 374 }{ 3 } - \frac{ 36 }{ 3 }\]

\[w = \frac{ 338 }{ 3 }\]

Answer 14

Do you understand how I got this?

Answer 15

yes
thanks

Answer 16

No problem :)

Answer 17

The formula for the circumference of a circle is 4072-01-01-03-00_files/i0150000.jpg. Determine the circumference when the radius r is 10 cm.
a.
1004072-01-01-03-00_files/i0150001.jpg cm
c.
20 cm
b.
204072-01-01-03-00_files/i0150002.jpg cm
d.
100 cm

Answer 18

http://prntscr.com/kxpi95

Answer 19

Follow my instagram: Therealvalenciia

Answer 20

What is the correct term for a large number of species in an ecosystem?

Answer 21

just wanna confirm something in Mandarin: when talking about the year 2XXX we use

Answer 22

Which book is considered the catalyst of the modern environmental movement?
Rachel Carsonu2019s ______________is considered the catalyst of the modern envir

Answer 23

Need help with a concept

Answer 24

Ooo

Answer 25

http://prntscr.com/kxhc6j

Answer 26

Orgo II Tutorial: Tosylates, Mesylates, Triflates

Answer 27

Orgo II Tutorial: Synthesis of Alkyl Halides with PBr/SOCl2

Answer 28

http://prntscr.com/kxgygd

Answer 29

http://prntscr.com/kxfnbk

Answer 30

http://prntscr.com/kxer5v

Answer 31

Show that

Answer 32

prove that 1/tan3x+tanx-1/cot3x+cotx=cot4x

Answer 33

A committee with members from both the House of Representatives and the Senate is called a __________.

Answer 34

A committee with members from both the House of Representatives and the Senate is called a __________.

Answer 35

Match the scenario to the type of mental health issue described.

Answer 36

Anyone looking forward to SAO's Alicization Arc? There's a speculation of around