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VMariaS [17]
3 years ago
5

PLEASE SOMEONE HELP ME

Mathematics
1 answer:
Soloha48 [4]3 years ago
8 0

9514 1404 393

Answer:

  a) 5 cm

  b) 8 cm

  c) 9 m

Step-by-step explanation:

It can be worthwhile to work the last attachment (a) first, since these are all variations of the same triangle.

The Pythagorean theorem tells you the sum of the squares of the legs is the square of the hypotenuse.

<u>Problem 6a</u>:

  3² +4² = x² . . . . fill in the given numbers; all measures in cm

  9 + 16 = x² . . . . simplify exponents

  25 = x² . . . . . . . simplify sum

  x = √25 = 5 . . . take the square root.

  x = 5 cm . . . . . . apply units

__

Note that this triangle is a 3-4-5 right triangle. That is a set of side lengths (ratios) that is useful to remember. In this problem set, you see it again immediately.

__

<u>Problem 6b</u>:

Shortest-to-longest, the side ratios of the given triangle are ...

  6 : x : 10

For some x', this is ...

  3 : x' : 5 . . . . . . . . . . . . . matches a 3-4-5 triangle with x' = 4

The scale factor is 6/3 = 10/5 = 2, so we have ...

  x = 2·x' = 2·4 = 8

  x = 8 cm . . . . . with units

__

<u>Problem 6c</u>:

The side ratios are ...

  x : 12 : 15  which reduces to  x' : 4 : 5

This matches a 3-4-5 triangle with x' = 3, and a scale factor of 12/4 = 15/5 = 3.

Then ...

  x = 3·x' = 3·3 = 9

  x = 9 m . . . . . with units

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