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son4ous [18]
3 years ago
14

In the image shape ABCD is similar to shape MNOP

Mathematics
2 answers:
DiKsa [7]3 years ago
4 0

Answer:

10.5

Step-by-step explanation:

cross multiplying:

?/12 = 14/16

16? = 168

? = 10.5

finlep [7]3 years ago
3 0

Answer: 10.5 inches.

Step-by-step explanation:

  • We know that if two polygons are similar to each other than the corresponding sides are proportional.

Given : In the image shape ABCD is similar to shape MNOP .

Then , AB corresponds to MN .

BC corresponds to NO.

CD corresponds to OP.                (1)

AD corresponds to MP.                 (2)

In the given figure we have ,

AD = 14 in.   , CD= 16 in. and OP =12 in.

To find : MP

Since shape ABCD is similar to shape MNOP then the corresponding sides should be proportional.

i.e. \dfrac{MP}{AD}=\dfrac{OP}{CD}  [By using (1) and (2)]

Substitute the values.

i.e. \dfrac{MP}{14}=\dfrac{12}{16}

i.e. MP=\dfrac{12}{16}\times14=10.5\ in.

Hence, the length of MP= 10.5 in.

Thus the correct answer is 10.5 inches.

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_____

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<em>Comment on the figure</em>

The usual geometry here is that the outside legs (opposite the vertical angles) are parallel, meaning that the angle indicators are the correct marks. It is possible, but unusual, for the red hash marks to be correct and the angle indicators to be mismarked. The red hash marks seem tentatively drawn, so seem like they're more likely to be the incorrect marks.

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