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den301095 [7]
3 years ago
14

What is the approximate length?

Mathematics
1 answer:
Usimov [2.4K]3 years ago
4 0

9514 1404 393

Answer:

  (a)  75.5

Step-by-step explanation:

There are two ways you can work this.

<u>Pythagorean theorem</u>

Triangle CMP is a right triangle. CM = AC = 55. CP = CB -PB = 55 -15 = 40. Then length PM can be found from ...

  PM² +CP² = CM²

  PM = √(CM² -CP²) = √(55² -40²) = √1425 ≈ 37.749

The length MN is twice the length of PM, so is ...

  MN = 2×PM = 2×37.349 = 75.498

The length of MN is about 75.5.

__

<u>Using chord relationships</u>

The products of the different lengths for the same chord are the same for the crossed chords.

  AP×PB = MP×PN

We know MP = PN, so ...

  MP = √(AP×PB) = √((55+40)(15)) = √1425

As before, MN = 2×MP = 2√1425

  MN ≈ 75.5

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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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