I need help please.

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  a) 191 yards

  b) 40 yards

  c) 1.5 minutes

Step-by-step explanation:

Given:

  ΔPQR is a right triangle with the right angle at Q

  PQ = 40 yards; QR = 70 yards

  M is the midpoint of PR

  jogging rate is 150 yd/min

Find:

  a) the perimeter of ΔPQR to the nearest yard

  b) QM to the nearest yard

  c) the time to jog the path PQMRQP to the nearest tenth minute

Solution:

a) The length of PR can be found from the Pythagorean theorem:

  PR² = PQ² +QR²

  PR² = 40² +70² = 6500

  PR = √6500 ≈ 80.62 . . . . yards

Then the perimeter is ...

  perimeter = PQ +QR +PR = 40 +70 +80.62 ≈ 191 yards

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b) Segment QM divides triangle PQR into two isosceles triangles: PMQ and RMQ. The lengths MP, MQ, and MR are all equal to half the length of PR.

  QM = PR/2 = (80.62 yd)/2 = 40.31 yd

  QM ≈ 40 yd

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c) The segments of path PQMRQP can be grouped to simplify the computation of the path length

  PQMRQP = PQ +QM +MR +RQ +QP = PQ +(PQ +QR +(QM +MR))

Since QM +MR = PR, the length in the outer parentheses is the perimeter of the triangle. Then the jogger's total path length is ...

  PQ + perimeter(ΔPQR) = 40 yd +191 yd = 231 yd

The time it takes to jog that path is ...

  time = distance/speed

  time = 231 yd/(150 yd/min) = 1.54 min ≈ 1.5 min

It takes about 1.5 minutes.

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step-by-step explanation:

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