Question 115500This question is from textbook Prentice Hall Mathematics
: find the value of x and y in the parallelogram PQRS
the diagonals of the parallelogram are QS and RP,and they bisect at point T. QT=3x, RT=y+3, PT=2x, and ST=2y
I have done number 18, and I have been working on this one for probably half an hour. I just don't know how to get the answer from the information given.
Thank you!
This question is from textbook Prentice Hall Mathematics
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! If I understand your problem correctly, the most critical information you need to use is that
the diagonals bisect each other. From this you know that:
.
QT = ST and
RT = PT
.
For the top equation you can substitute 3x for QT and 2y for ST to make the equation:
.
3x = 2y
.
For the bottom equation you can substitute y + 3 for RT and 2x for PT and it becomes:
.
y + 3 = 2x
.
So you have the two equations:
.
3x = 2y and
y + 3 = 2x
.
Let's solve them by substitution. Solve the bottom equation for y by subtracting 3 from both
sides to end up with:
.
y = 2x - 3
.
Now go to the top equation [3x = 2y] and substitute 2x - 3 for y to get:
.
3x = 2(2x - 3)
.
Multiply out the right side:
.
3x = 4x - 6
.
get rid of the 6 on the right side by adding 6 to both sides and you have:
.
3x + 6 = 4x
.
Subtract 3x from both sides and you finally get to:
.
6 = x
.
Now that you know x = 6 you can return to either of the two original equations, substitute 6 for
x, and solve for y. Let's return to the equation 2y = 3x and substitute 6 for x to get:
.
2y = 3*6
.
Multiply out the right side:
.
2y = 18
.
Solve for y by dividing both sides by 2 to get:
.
y = 9
.
In summary, we've found that x = 6 and y = 9
.
Let's check. From the geometry we know PT should equal RT. PT is 2x which is 2*6 or 12. RT is y + 3
which is 9 + 3 = 12. Line PR is bisected at T because both PT and RT equal 12.
.
Also from the geometry we know that QT should equal ST. QT = 3x = 3*6 = 18. And ST = 2y = 2*9 = 18.
This means that diagonal QS is bisected at T because both QT and ST equal 18.
.
Hope this helps you to understand the problem and how to get the answers for x and y.
.
|
|
|
