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
- The value of x is 5 or 12
- The distance between Bristol and Chester is either <em>5 miles or 12 miles</em>
Let:
A represents Amory
B represents Bristol
C represents Chester
<u>(a) The unknown quantity</u>
From the question, we understand that:
<em /><em> --- from Amory to Bristol, through Chester</em>
<em /><em> --- directly from Amory to Bristol (and you save 4 miles)</em>
<em />
So, we have:
Let the distance from Bristol to Chester be x.
<u>(b) The sketch</u>
See attachment for the illustration
<u>(c) An equation about the variable</u>
Using Pythagoras theorem, we have:
So, we have:
<u>(d) Solve the equation</u>
In (c), we have:
Evaluate the exponents
Collect like terms
Divide through by 2
Expand
Factorize
Factor out x - 12
Solve for x
<u>(e) The distance between Bristol and Chester</u>
The above values of x means that:
The distance between Bristol and Chester is either <em>5 miles or 12 miles</em>
<em />
Read more about Pythagoras equations at:
brainly.com/question/23936129