SOLUTION: In rectangle ABCD, diagonal AC = 5x and diagonal BD = 6x – 2. Find x and then find the length of AC.

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Question 289103: In rectangle ABCD, diagonal AC = 5x and diagonal BD = 6x – 2. Find x and then find the length of AC.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In any rectangle, the diagonals are equal. So diagonal AC = diagonal BD. This then means that 5x=6x-2


Solved by pluggable solver: Linear Equation Solver


5x=6x-2 Start with the given equation.



5x-6x=-2 Subtract 6x from both sides.



-x=-2 Combine like terms on the left side.



x=%28-2%29%2F%28-1%29 Divide both sides by -1 to isolate x.



x=2 Reduce.



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Answer:

So the solution is x=2





Since x=2, this means that AC=5x=5%282%29=10 and BD=6x-2=6%282%29-2=12-2=10. So we can see that both AC and BD are 10 units long. This verifies our answer.