X=5, y=7 X=6, y=9 X=6, y=8 X=7, y=10

Mathematics

1 answer:

Zinaida [17]3 years ago

3 0

The answer is x=6, y=9.

EXPLANATION

Segments QT and ST are congruent to each other because the diagonals meet at point T, which bisects them. Segments RT and PT are also congruent.

Deriving from this, we say

QT = ST
PT = RT

Choose one of these diagonals, so we can simply find one value of x we can substitute for another diagonal.

So, in this case, we use first PT = RT

PT = RT
2x = y+3
x=(y+3)/2

Now, we will plug in the value of x to the equation showing the congruence of segments QT = ST.

QT = ST
3x = 2y
3(y+3)/2 = 2y
3y+9/2 = 2y
(3y+9/2 = 2y)2
3y+9 = 4y
y = 9

Now, we have the value of y, substitute it to any of the two equations we had for the two diagonals.

2x = y+3
2x = 9+3
2x = 12
x = 6

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