Question

In the figure below,

PT = x + 2
TR = y
QT = 2x
and TS = y + 3

(picture attached below)

find the values of x and y in parallelogram PQRS.

A. x = 2, y = 1
B. x = 1, y = 3
C. x = 4, y = 5
D. x = 5, y = 7

thanks in advance! :)

Answer 1

similar to the last problem
y = x + 2
y + 3 = 2x

so we need to find which values fit

check out B and D - its one of those

Answer 2

Option D is correct

x = 5 , y = 7

Explanation:

Properties of parallelogram:

Diagonal bisects each other.

In other way, we can say that the diagonal intersects each other at half-way point.

As per the given statement:

PT = x + 2

TR = y

QT = 2x and TS = y + 3

From the given figure:

In parallelogram PQRS:

By properties we have;

PT = TR

QT = TS

Substitute the given values we have;

`x+2 = y` .....[1]

`2x = y+3` .....[2]

Substitute equation [1] into [2] we have;

`2x = x+2+3`

⇒2x = x+5

Subtract x from both sides we have;

x = 5

Substitute x = 5 in [1] we have;

5+2 = y

7 = y

or

y= 7

Therefore, the value of x and y are:

x = 5 , y = 7