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AveGali [126]
2 years ago
15

in the figure below trianglePQM and triangleQRP are right triangles. the measure of lineQM is 6 and the measure of lineQP is 8.

what is the measure of line PR?

Mathematics
1 answer:
Kipish [7]2 years ago
3 0

Answer:

Option 4 is correct. The length of PR is 6.4 units.

Step-by-step explanation:

From the given figure it is noticed that the triangle PQR and triangle MQR.

Let the length of PR be x.

Pythagoras formula

hypotenuse^2=base^2+perpendicular^2

Use pythagoras formula for triangle PQM.

PM^2=QM^2+PQ^2

PM^2=(6)^2+(8)^2

PM^2=36+64

PM^2=100

PM=10

The value of PM is 10. The length of PR is x, so the length of MR is (10-x).

Use pythagoras formula for triangle PQR.

PQ^2=QR^2+PR^2

(8)^2=QR^2+x^2

64-x^2=QR^2                   .....(1)

Use pythagoras formula for triangle MQR.

MQ^2=QR^2+MR^2

(6)^2=QR^2+(10-x)^2

36=QR^2+x^2-20x+100

36-x^2+20x-100=QR^2        .... (2)

From equation (1) and (2) we get

36-x^2+20x-100=64-x^2

20x-64=64

20x=128

x=6.4

Therefore length of PR is 6.4 units and option 4 is correct.

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