The lengths of the three sides of a triangle are given. Which of these is a right triangle?
6,7 and 8
14, 15 and 16
17,144 and 145
27,264 and 265

answer:

Step-by-step explanation:

If you had two workers performing at different rates, to find their total rate you would look at the problem like this:

rate A + rate B = total rate

work A = rate A * time

work B = rate B * time

total work = work A + work B

total work = rate A * time + rate B * time

factoring out the time gives you

total work = time * (rate A + rate B)

Now, let's apply these concepts to the problem

Let A = Alice's rate (jobs/hr)

Let B = Bob's rate (jobs/hr)

Let C = Charlie's rate (jobs/hr)

So, if Alice and Bob can do one job in 2 hours, their equation would be:

2hrs•(A jobs/hr + B jobs/hr) = 1 job or just simply

2•(A + B) = 1 which becomes

2A + 2B = 1 [EQUATION 1]

For Alice and Charlie the equation would be:

3•(A + C) = 1 which becomes

3A + 3C = 1 [EQUATION 2]

For Bob and Charlie the equation would be:

4•(B + C) = 1 which becomes

4A + 4C = 1 [EQUATION 3]

Now you have a system of equations with three equations and three unknowns:

2A + 2B = 1 [EQUATION 1]

3A + 3C = 1 [EQUATION 2]

4B + 4C = 1 [EQUATION 3]

Let's solve [EQUATION 1] for A and substitute that into [EQUATION 2]

2A + 2B = 1

2A = 1 - 2B

A = (1/2) - B [EQUATION 1]*

3A + 3C = 1

3[(1/2) - B] + 3C = 1

(3/2) - 3B + 3C = 1

- 3B + 3C = 1 - (3/2)

- 3B + 3C = (2/2) - (3/2)

- 3B + 3C = - (1/2) [EQUATION 2]*

Now, combine [EQUATION 2]* and [EQUATION 3] and use the elimination method to solve for one of the variables

- 3B + 3C = - (1/2) [EQUATION 2]*

4B + 4C = 1 [EQUATION 3]

4•[- 3B + 3C = - (1/2)] [EQUATION 2]*

3•[ 4B + 4C = 1] [EQUATION 3]

- 12B + 12C = - 2 [EQUATION 2]*

12B + 12C = 3 [EQUATION 3]

24C = 1

C = 1/24 jobs/hr

Substituting C into [EQUATION 3]

4B + 4C = 1 [EQUATION 3]

4B + 4•(1/24) = 1

4B + (4/24) = 1

4B + (1/6) = 1

4B = 1 - (1/6)

4B = 5/6

B = 5/24 jobs/hr

Substituting B into [EQUATION 1]

2A + 2B = 1 [EQUATION 1]

2A + 2•(5/24) = 1

2A + 10/24 = 1

2A + 5/12 = 1

2A = 1 - 5/12

2A = 7/12

A = 7/24 jobs/hr

Working together their total rate would be:

(7/24) + (5/24) + (1/24) = 13/24 jobs/hr

Since work = rate × time

1 (job) = 13/24 (jobs/hr) × time (hrs)

Solving for time gives time = 1/[(13/24)] = 24/13 hrs = 1 11/13 hrs