Question

1.Measurement of segment QR is 2Measurement of segment TS is 3.Measurement if segment QT is

Answer 1

In a parallelogram, opposite sides are of equal measure.

QR = TS

find x

• 5(x) - 1 = 2(x) + 5

• 5(x) - 2(x) = 5 + 1

• 3(x) = 6

• x = 2

1)

• QR:

• 5(x) - 1

• 5(2) - 1

• 10 - 1

• 9

2)

• QR = TS = 9

Find value of y:

• QT = RS

• y + 8 = 3(y) - 2

• y - 3(y) = -2 - 8

• -2(y) = -10

• y = 5

3)

QT:

• y + 8

• 5 + 8

• 13

4)

if x = 5

means the diagram is enlarged.

• scale factor = 5/2 = 2.5

then y will be:

• 2.5 * 5 = 12.5

Answer 2

We need x and y

Opposite sides of a parallelogram are equal

• QR=TS
• 5x-1=2x+5
• 3x=6
• x=2

And

• RS=QT
• 3y-2=y+8
• 2y=10
• y=5

Hence

• QR=TS=5x-1=5(2)-1=9
• RS=QT=y+8=5+8=13

#3

Segment QT is 4

so

• y+8=4
• y=4+8
• y=12

Another way

• x is 5

• old x is 2

So

scale factor:-

• k=5/2=2.5

Find y

• y=5k
• y=5(2.5)
• y=12.5