Solving Similar Triangles
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Question 1 of 5
1. Question
The following two triangles are similar.Solve for the missing sides `x` and `y`
- `x=` (6) `y=` (4)
Hint
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Well Done!
Incorrect
First, identify corresponding sides and angles of the two triangles.
Write out the proportions of corresponding sides to solve for `x`$$\frac{\color{#e85e00}{QP}}{\color{#e85e00}{MN}}=\frac{\color\green{x}}{\color\green{ON}}$$ Definition of Similarity $$\frac{\color{#e85e00}{15}}{\color{#e85e00}{5}}=\frac{\color\green{x}}{\color\green{2}}$$ Plug in the side lengths `2 xx 15` `=` `5 xx x` Cross Multiply `30``divide 5` `=` `5x``divide 5` Divide both sides by `5` `6` `=` `x` `x` `=` `6` Do the same to solve for `y`$$\frac{\color{#e85e00}{QP}}{\color{#e85e00}{MN}}=\frac{\color{#004ec4}{RP}}{\color{#004ec4}{y}}$$ Definition of Similarity $$\frac{\color{#e85e00}{15}}{\color{#e85e00}{5}}=\frac{\color{#004ec4}{12}}{\color{#004ec4}{y}}$$ Plug in the side lengths `y xx 15` `=` `5 xx 12` Cross Multiply `15y` `=` `60` `15y``divide 15` `=` `60``divide 15` Divide both sides by `15` `y` `=` `4` `x=6` and `y=4` -
Question 2 of 5
2. Question
The following two triangles are similar.Solve for the missing side `y`
- `y=` (24)
Hint
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Nice Job!
Incorrect
First, seperate the two triangles.
Write out the proportions of corresponding sides to solve for `y`$$\frac{\color{#e85e00}{BC}}{\color{#e85e00}{DE}}=\frac{\color\green{y}}{\color\green{AD}}$$ Definition of Similarity $$\frac{\color{#e85e00}{6}}{\color{#e85e00}{2}}=\frac{\color\green{y}}{\color\green{8}}$$ Plug in the side lengths `6 xx 8` `=` `2 xx y` Cross Multiply `48` `=` `2y` `48``divide 2` `=` `2y``divide 2` Divide both sides by `2` `24` `=` `y` `y=24` -
Question 3 of 5
3. Question
The following two triangles are similar.Solve for the missing sides `x` and `y`
- `x=` (5.88) `y=` (5.9)
Hint
Help VideoCorrect
Excellent!
Incorrect
First, seperate the two triangles.
Write out the proportions of corresponding sides to solve for `x`$$\frac{\color{#e85e00}{AB}}{\color{#e85e00}{AE}}=\frac{AC}{\color\green{AD}}$$ Definition of Similarity $$\frac{\color{#e85e00}{22}}{\color{#e85e00}{5}}=\frac{x+20}{\color\green{x}}$$ Plug in the side lengths `5 xx (x+20)` `=` `22 xx x` Cross Multiply `5x +100` `=` `22x` Simplify `100` `=` `17x` `100``divide 17` `=` `17x``divide 17` Divide both sides by `17` `5.88` `=` `x` Do the same on corresponding sides to solve for `y`$$\frac{\color{#e85e00}{5}}{\color{#e85e00}{22}}=\frac{\color{#004ec4}{y}}{\color{#004ec4}{26}}$$ Plug in the side lengths `22 xx y` `=` `5 xx 26` Cross Multiply `22y` `=` `130` Simplify `22y``divide 22` `=` `130``divide 22` Divide both sides by `22` `y` `=` `5.9` `x=5.88` and `y=5.9` -
Question 4 of 5
4. Question
The following two triangles are similar.Solve for the missing side `x`
- `x=` (7)
Hint
Help VideoCorrect
Fantastic!
Incorrect
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`$$\frac{\color{#e85e00}{AE}}{\color{#e85e00}{AB}}=\frac{\color\green{ED}}{\color\green{x}}$$ Definition of Similarity $$\frac{\color{#e85e00}{6}}{\color{#e85e00}{14}}=\frac{\color\green{3}}{\color\green{x}}$$ Plug in the side lengths `6 xx x` `=` `3 xx 14` Cross Multiply `6x``divide 6` `=` `42``divide 6` Divide both sides by `6` `x` `=` `7` `x=7` -
Question 5 of 5
5. Question
The following two triangles are similar.Solve for the missing side `y`
- `y=` (4.8)
Hint
Help VideoCorrect
Keep Going!
Incorrect
First, seperate the two triangles.
Write out the proportions of corresponding sides to solve for `y`$$\frac{\color{#e85e00}{EB}}{\color{#e85e00}{BC}}=\frac{\color\green{AB}}{\color\green{y}}$$ Definition of Similarity $$\frac{\color{#e85e00}{20}}{\color{#e85e00}{8}}=\frac{\color\green{12}}{\color\green{y}}$$ Plug in the side lengths `12 xx 8` `=` `20 xx y` Cross Multiply `96` `=` `20y` `96``divide 20` `=` `20y``divide 20` Divide both sides by `20` `4.8` `=` `y` `y=4.8`