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AleksAgata [21]
3 years ago
7

Use the triangles to find the missing length of segment TU.

Mathematics
1 answer:
Lapatulllka [165]3 years ago
5 0

Answer: Option C is the correct answer.

Step-by-step explanation:

Triangle STU is similar to triangle SVW. This means that the ratio of the length of each side of ∆STU to the length of the corresponding side of ∆ SVW is constant. Therefore,

ST/SV = TU/VW = SU/SW

SV = 12 + 18 = 30 in

Therefore,

12/30 = TU/40

Cross multiplying, it becomes

TU × 30 = 12 × 40

30TU = 480

Dividing the left hand side and the right hand side of the equation by 30, it becomes

30TU/30 = 480/30

TU = 16

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What is the area of parallelogram ABCD?<br><br><br> ____ square units
valentinak56 [21]

Answer:

13

Step-by-step explanation:

Here's a method of finding the area of any polygon knowing its vertices. I'm using this parallelogram as an example.

Make a table like this (each vertex with its x- and y-coordinates):

Pt    x       y

A     3      6

B     6      5

C     5      1

D     2      2

A     3      6

Now multiply each x-coordinate by the y-coordinate on the line below and write it on the right side. Bold type shows the first multiplication.

       x       y

A     3      6

B     6      5      15

C     5      1        6

D     2      2      10

A     3      6      12

Now multiply each y-coordinate by the x-coordinate on the line below and subtract from each produce you already have. Do each subtraction. Bold type shows the first multiplication.

       x       y

A     3     6

B     6      5      15 - 36 = -21

C     5      1        6 - 25 = -19

D     2      2      10 - 2 =     8

A     3      6      12 - 6 =     6

Add all the differences.

       x       y

A     3      6

B     6      5      15 - 36 = -21

C     5      1        6 - 25 = -19

D     2      2      10 - 2 =     8

A     3      6      12 - 6 =     6

                                   +____

                                       -26

The area of the polygon is the absolute value of half of the sum of the differences.

area = |-26/2| = |-13| = 13

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Since they are congruent rectangles, they have the same side lengths.
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