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Pythagoras Theorem Mixed Review 1Pythagoras Theorem Mixed Review 1
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Question 1 of 4
1. Question
Find the value of the missing length `c`
The given measurements are in units- `c=` (5)` \text(units)`
Hint
Help VideoCorrect
Well Done!
Incorrect
Pythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` are the two sides, and `c` is the hypotenuseLabelling each length of the triangle
Use the Pythagorean Theorem Formula to solve for `c``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `3^2``+``4^2` `=` `c^2` Plug in the known lengths `9+16` `=` `c^2` Evaluate `sqrt(c^2)` `=` `sqrt25` Take the square root of both sides `c` `=` `5 \text(units)` `c=5 \text(units)` -
Question 2 of 4
2. Question
Find the value of the missing length `k`
The given measurements are in units- `k=` (9)` \text(units)`
Hint
Help VideoCorrect
Great Work!
Incorrect
Method One
Finding a Side
Use $$\large\textbf{-}$$
$${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$$Use the formula for Finding a Side to solve for `k`$${\color{#9a00c7}{a}}^2$$ `=` $${\color{#00880a}{c}}^2-{\color{#007DDC}{b}}^2$$ Finding a Side $${\color{#9a00c7}{k}}^2$$ `=` $${\color{#00880a}{15}}^2-{\color{#007DDC}{12}}^2$$ Plug in the known lengths `k^2` `=` `225-144` Evaluate `k^2` `=` `81` `sqrt(k^2)` `=` `sqrt81` Take the square root of both sides `k` `=` `9 \text(units)` `k=9 \text(units)`Method TwoPythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` can be switched as they are both sidesLabelling each length of the triangle
Use the Pythagorean Theorem Formula to solve for `k``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `k^2``+``12^2` `=` `15^2` Plug in the known lengths `k^2+144` `=` `225` Evaluate `k^2+144` `-144` `=` `225` `-144` Subtract `144` from both sides `k^2``+144` `-144` `=` `81` `144-144` cancels out `sqrt(k^2)` `=` `sqrt81` Take the square root of both sides `k` `=` `9 \text(units)` `k=9 \text(units)` -
Question 3 of 4
3. Question
Find the value of the missing length `x`
Round your answer to 2 decimal places- `x=` (11.66) `\text(cm)`
Hint
Help VideoCorrect
Nice Job!
Incorrect
Pythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` are the two sides, and `c` is the hypotenuseLabelling each length of the triangle
Use the Pythagorean Theorem Formula to solve for `c``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `6^2``+``10^2` `=` `x^2` Plug in the known lengths `36+100` `=` `x^2` Evaluate `sqrt(x^2)` `=` `sqrt136` Take the square root of both sides `x` `=` `11.66 \text(cm)` Rounded to two decimal places `x=11.66 \text(cm)` -
Question 4 of 4
4. Question
Find the value of the missing length `y`
Round your answer to 2 decimal places- `y=` (14.42)` \text(cm)`
Hint
Help VideoCorrect
Excellent!
Incorrect
Pythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` are the two sides, and `c` is the hypotenuseLabelling each length of the triangle
Use the Pythagorean Theorem Formula to solve for `c``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `8^2``+``12^2` `=` `y^2` Plug in the known lengths `64+144` `=` `y^2` Evaluate `sqrt(y^2)` `=` `sqrt208` Take the square root of both sides `y` `=` `14.42 \text(cm)` Rounded to two decimal places `y=14.42 \text(cm)`
Quizzes
- Find the Hypotenuse 1
- Find the Hypotenuse 2
- Find the Hypotenuse 3
- Find a Side 1
- Find a Side 2
- Find a Side 3
- Pythagoras Problems 1
- Pythagoras Problems 2
- Pythagoras Problems 3
- Pythagoras Theorem Mixed Review 1
- Pythagoras Theorem Mixed Review 2
- Pythagoras Theorem Mixed Review 3
- Pythagoras Theorem Mixed Review 4