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# Polygon Equations - Checking my homework.

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

Oct 8, 2019
#2
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I fixed the link so it must work now. Can you help me?

Guest Oct 8, 2019
#3
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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

Oct 8, 2019
#4
+109563
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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

Oct 9, 2019
#5
+109563
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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

Oct 9, 2019
#6
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Thank you so much! I checked my work and corrected it.

Guest Oct 9, 2019
#7
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OK....good deal   !!!

CPhill  Oct 9, 2019