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Lesson 23 godine by og
Activity 3 Application
The town of Amory lies due north of Chester, and Bristol lies due east of
Chester. If you drive from Amory to Bristol by way of Chester, the distance is 17
miles, but if you take the back road
directly from
Amory to Bristol, you save 4
miles. You would like to know the distance from Bristol to Chester,
a. What is the unknown quantity? Call it.
b. Make a sketch and label it with distances,
c. Write an equation about the variable
d. Solve your equation.
e. How far is it from Bristol to Chester?

Sagot :

MrRoyal

The distance between the three places is an illustration of Pythagoras theorem.

  • The unknown quantity is the distance from Bristol to Chester
  • See attachment for sketch
  • The equation about the variable is [tex]\mathbf{13^2 = x^2 + (17 - x)^2}[/tex]
  • The value of x is 5 or 12
  • The distance between Bristol and Chester is either 5 miles or 12 miles

Let:

A represents Amory

B represents Bristol

C represents Chester

(a) The unknown quantity

From the question, we understand that:

[tex]\mathbf{AC + CB = 17}[/tex] --- from Amory to Bristol, through Chester

[tex]\mathbf{AB = 17 - 4}[/tex] --- directly from Amory to Bristol (and you save 4 miles)

So, we have:

[tex]\mathbf{AB = 13}[/tex]

Let the distance from Bristol to Chester be x.

(b) The sketch

See attachment for the illustration

(c) An equation about the variable

Using Pythagoras theorem, we have:

[tex]\mathbf{AB^2 = BC^2 + AC^2}[/tex]

So, we have:

[tex]\mathbf{13^2 = x^2 + (17 - x)^2}[/tex]

(d) Solve the equation

In (c), we have:

[tex]\mathbf{13^2 = x^2 + (17 - x)^2}[/tex]

Evaluate the exponents

[tex]\mathbf{169 = x^2 + 289 - 34x + x^2}[/tex]

Collect like terms

[tex]\mathbf{x^2 + x^2 - 34x + 289 -169 = 0 }[/tex]

[tex]\mathbf{2x^2 - 34x + 120= 0 }[/tex]

Divide through by 2

[tex]\mathbf{x^2 - 17x + 60= 0 }[/tex]

Expand

[tex]\mathbf{x^2 - 12x - 5x + 60= 0 }[/tex]

Factorize

[tex]\mathbf{x(x - 12) - 5(x - 12)= 0 }[/tex]

Factor out x - 12

[tex]\mathbf{(x - 5)(x - 12)= 0 }[/tex]

Solve for x

[tex]\mathbf{x - 5 = 0\ or\ x - 12= 0 }[/tex]

[tex]\mathbf{x = 5\ or\ x = 12 }[/tex]

(e) The distance between Bristol and Chester

The above values of x means that:

The distance between Bristol and Chester is either 5 miles or 12 miles

Read more about Pythagoras equations at:

https://brainly.com/question/23936129

View image MrRoyal
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