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Assume that in each pair of figures, the second polygon is similar to the first, with the same orientation. Perform these steps.

  • Set up equations to find the lengths of the sides labeled by variables. 
  • Solve each equation and find the labeled lengths.
  • Find any remaining lengths of either figure.

Click to view Image: https://imgur.com/a/zxpVuBS​

 

Can someone please solve them if my work is right? Thanks.

 Oct 8, 2019
edited by Guest  Oct 8, 2019
 #1
avatar+106536 
0

The image(s) doesn't/don't display for me when I pull up the link.....

 

 

 

cool cool cool

 Oct 8, 2019
 #2
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0

I fixed the link so it must work now. Can you help me?

Guest Oct 8, 2019
 #3
avatar+106536 
+2

1.   We have that

 

6/9  =  t / [ t + 2 ]    cross-multiply

 

6 [ t + 2]  = 9t

 

6t + 12  =  9t    subtract 6t from both sides

 

12  =  3t          divide both sides by 3

 

4  =  t

 

t + 2  =  6

 

We can find the missing side S  of the figure on the right, thusly

 

11/9  = S /[ t + 2]

 

11/9  =  S  / 6      cross-multiply

 

11* 6  =  9S

 

66 =  9S       divide both sides by   9

 

66/9  =  S   =  22/3

 

 

cool cool cool

 Oct 8, 2019
 #4
avatar+106536 
+2

2. 

 

6/8  =  [ w - 5 ] / w     cross-multiply

 

6w  =  8 [ w - 5 ]

 

6w  =  8w - 40       subtract 8w  from both sides

 

-2w  = -40        divide both sides by  -2

 

w  =  20

 

w - 5  =  15

 

 

To find one missing side  in the second figure that would be the couter-part to the side of 9 in the first figure we have that

 

Missing side/ w  =   9/8

 

Missing side 20  =  9/8      multiply both sides by 20

 

Missing side  =  20 * 9 / 8   =  180 / 8  = 22.5

 

And to find the last missing side of the second figure that is a counter-part to the side of 14 in the first figure we have that

 

Missing side / 22.5  = 14/ 9

 

Missing side  =  22.5 * 14 / 9   =    35

 

cool cool cool

 Oct 9, 2019
 #5
avatar+106536 
+2

3.  

 

t/ 4  = [ t + 1 ]  / 6      cross-multiply

 

6t  =  4 [ t + 1 ]

 

6t  =  4t + 4       subtract  4t from both sides

 

2t  =  4   divide both sides by 2

 

t  = 2

 

t + 1  =  3

 

To find the remaining missing side in the first figure we have that

 

Missing side / t  =   10/ [ t + 1 ]

 

Missing side / 2  =  10/ 3    

 

Missing side  =   2 * 10  / 3  =   20/3

 

cool cool cool

 Oct 9, 2019
 #6
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+1

Thank you so much! I checked my work and corrected it. laugh

Guest Oct 9, 2019
 #7
avatar+106536 
0

OK....good deal   !!!

 

cool cool cool

CPhill  Oct 9, 2019

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