The required values of x and y are x = 2 and y = 11.
We have been given that parallelogram PQRS which has:
PT = y, TR = 5x+1, QT = 2y, TS = 6x+10
We know that the diagonals of a parallelogram bisect each other.
So, PT = TR and QT = TS
Substitute the values and we have a system of equations:
y = 5x + 1 ....(i)
2y = 6x + 10 ....(ii)
Substitute the value of the equation y = 5x + 1 in equation (ii), and solve for x
2(5x + 1) = 6x + 10
10x + 2 = 6x + 10
10x - 6x = 10 - 2
4x = 8
x = 8/4
x = 2
Substitute the value of x = 2 in equation (i), and solve for y
y = 5(2) + 1
y = 10 + 1
y = 11
Therefore, the required values of x and y are x = 2 and y = 11.
Learn more about parallelograms here:
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