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25 votes
25 votes
Using proportions to solve for missing sides.
RST~YSZ, find YZ.

Using proportions to solve for missing sides. RST~YSZ, find YZ.-example-1
User Ayo I
by
3.0k points

1 Answer

8 votes
8 votes

Answer:

YZ = 28

Explanation:

A proportion involving the known and unknown sides is ...

TR/ST = ZY/SZ

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This proportion uses SZ, which is not shown on the diagram. The length of SZ can be found from ...

SZ +ZT = ST . . . . . . . segment sum theorem

SZ + 5 = 40 . . . . with given values

SZ = 35 . . . . . subtract 5

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So, the proportion with values filled in is ...

(3x -7)/40 = (2x +2)/35

7(3x -7) = 8(2x +2) . . . . . . . multiply by 280

21x -49 = 16x +16 . . . . . . . eliminate parentheses

5x = 65 . . . . . . . . . . add 49 -16x

x = 13 . . . . . . . . divide by 5

YZ = 2x +2 = 2(13) +2

YZ = 28

_____

Additional comment

RT = 3x -7 = 3(13) -7 = 32

User Caduchon
by
2.9k points
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