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Given SUP ~ MAN. If SU=25, MA = 18, UP = x, and AN = 2x-5, then UP equals... Round answer to the nearest tenth.

Given SUP ~ MAN. If SU=25, MA = 18, UP = x, and AN = 2x-5, then UP equals... Round-example-1
User Haleksandre
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1 Answer

19 votes
19 votes
Answer:

UP = 3.9

Explanations:

△ SUP ~ △MAN (That is, △ SUP is similar to △MAN)

When two triangles are similar:

their corresponding sides have a common proportion (scale factor)

their corresponding angles are congruent

SP and MN are corresponding

UP and AN are corresponding

SU and MA are corresponding

SU = 25

MA = 18

UP = x

AN = 2x - 5

Since the triangles are similar, and for similarity, the ratio of corresponding sides shhould be the same:

UP / AN = SU / MA

x / (2x-5) = 25 / 18

Cross multiply:

18x = 25(2x - 5)

18x = 50x - 125

50x - 18x = 125

32x = 125

x = 125 / 32

x = 3.9

Since UP = x

UP = 3.9

User Calin Pirtea
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3.2k points