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Question 1 of 5
The following two triangles are similar.
Solve for the missing sides xx and yy
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First, identify corresponding sides and angles of the two triangles.
Write out the proportions of corresponding sides to solve for xx
QPMN=xONQPMN=xON |
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Definition of Similarity |
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155=x2155=x2 |
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Plug in the side lengths |
2×152×15 |
== |
5×x5×x |
Cross Multiply |
3030÷5÷5 |
== |
5x5x÷5÷5 |
Divide both sides by 55 |
66 |
== |
xx |
xx |
== |
66 |
Do the same to solve for yy
QPMN=RPyQPMN=RPy |
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Definition of Similarity |
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155=12y155=12y |
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Plug in the side lengths |
y×15y×15 |
== |
5×125×12 |
Cross Multiply |
15y15y |
== |
6060 |
15y15y÷15÷15 |
== |
6060÷15÷15 |
Divide both sides by 1515 |
yy |
== |
44 |
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Question 2 of 5
The following two triangles are similar.
Solve for the missing side yy
Incorrect
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First, seperate the two triangles.
Write out the proportions of corresponding sides to solve for yy
BCDE=yADBCDE=yAD |
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Definition of Similarity |
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62=y862=y8 |
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Plug in the side lengths |
6×86×8 |
== |
2×y2×y |
Cross Multiply |
4848 |
== |
2y2y |
4848÷2÷2 |
== |
2y2y÷2÷2 |
Divide both sides by 22 |
2424 |
== |
yy |
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Question 3 of 5
The following two triangles are similar.
Solve for the missing sides xx and yy
Incorrect
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First, seperate the two triangles.
Write out the proportions of corresponding sides to solve for xx
ABAE=ACADABAE=ACAD |
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Definition of Similarity |
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225=x+20x225=x+20x |
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Plug in the side lengths |
5×(x+20)5×(x+20) |
== |
22×x22×x |
Cross Multiply |
5x+1005x+100 |
== |
22x22x |
Simplify |
100100 |
== |
17x17x |
100100÷17÷17 |
== |
17x17x÷17÷17 |
Divide both sides by 1717 |
5.885.88 |
== |
xx |
Do the same on corresponding sides to solve for yy
522=y26522=y26 |
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Plug in the side lengths |
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22×y |
= |
5×26 |
Cross Multiply |
22y |
= |
130 |
Simplify |
22y÷22 |
= |
130÷22 |
Divide both sides by 22 |
y |
= |
5.9 |
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Question 4 of 5
The following two triangles are similar.
Solve for the missing side x
Incorrect
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First, seperate the two triangles.
Notice that length AB=14 since the sum of AE=6 and EB=8 is 14
Write out the proportions of corresponding sides to solve for x
AEAB=EDx |
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Definition of Similarity |
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614=3x |
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Plug in the side lengths |
6×x |
= |
3×14 |
Cross Multiply |
6x÷6 |
= |
42÷6 |
Divide both sides by 6 |
x |
= |
7 |
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Question 5 of 5
The following two triangles are similar.
Solve for the missing side y
Incorrect
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First, seperate the two triangles.
Write out the proportions of corresponding sides to solve for y
EBBC=ABy |
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Definition of Similarity |
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208=12y |
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Plug in the side lengths |
12×8 |
= |
20×y |
Cross Multiply |
96 |
= |
20y |
96÷20 |
= |
20y÷20 |
Divide both sides by 20 |
4.8 |
= |
y |