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lisabon 2012 [21]
3 years ago
8

The diagonals of a parallelogram QRST, TR And QS, Intersect at point U, if RS = 10 , ST=12,And RU=9.5 , Find The Perimeter Of Th

e parallelogram QRST.
A. 39
B. 44
C. 88
D.100

Mathematics
2 answers:
Bond [772]3 years ago
7 0
The answer is B. 44
alisha [4.7K]3 years ago
4 0

Answer:

(B)44

Step-by-step explanation:

It is given that The diagonals of a parallelogram QRST, TR And QS, Intersect at point U, if RS = 10 , ST=12,And RU=9.5.

Now, Since, RS =10, then RS=QT=10 (Opposite sides of parallelogram are equal).

And, ST=12, then ST=QR=12 (Opposite sides of parallelogram are equal)

Thus, The perimeter of the parallelogram QRST is given as:

Perimeter=Sum of all the sides

Perimeter=QR+RS+ST+TQ

Perimeter=12+10+12+10

Perimeter=44

Therefore, the perimeter of the given parallelogram QRST is 44 units.

Hence, option B is correct.

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Answer only if you know<br><br> HELP PART A AND PART B
VARVARA [1.3K]

Answers:

  • Part A) There is one pair of parallel sides
  • Part B) (-3, -5/2) and (-1/2, 5/2)

====================================================

Explanation:

Part A

By definition, a trapezoid has exactly one pair of parallel sides. The other opposite sides aren't parallel. In this case, we'd need to prove that PQ is parallel to RS by seeing if the slopes are the same or not. Parallel lines have equal slopes.

------------------------

Part B

The midsegment has both endpoints as the midpoints of the non-parallel sides.

The midpoint of segment PS is found by adding the corresponding coordinates and dividing by 2.

x coord = (x1+x2)/2 = (-4+(-2))/2 = -6/2 = -3

y coord = (y1+y2)/2 = (-1+(-4))/2 = -5/2

The midpoint of segment PS is (-3, -5/2)

Repeat those steps to find the midpoint of QR

x coord = (x1+x2)/2 = (-2+1)/2 = -1/2

y coord = (x1+x2)/2 = (3+2)/2 = 5/2

The midpoint of QR is (-1/2, 5/2)

Join these midpoints up to form the midsegment. The midsegment is parallel to PQ and RS.

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