Topics
>
Pre - Algebra>
Pythagoras' Theorem>
Pythagoras Theorem Mixed Review>
Pythagoras Mixed Review 3Pythagoras Mixed Review 3
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 4 questions completed
Questions:
- 1
- 2
- 3
- 4
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- Answered
- Review
-
Question 1 of 4
1. Question
ABCD is a square with `BD=18` cm. Find the length of `AB`.
Round your answer to 2 decimal places- `AB=` (12.73)` \text(cm)`
Hint
Help VideoCorrect
Exceptional!
Incorrect
Method One
Finding a Side
Use $$\large\textbf{-}$$
$${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$$Labelling each length of the triangle
All sides of a square are equal, so `a=b=AB`.Use the formula for Finding a Side to solve for `AB`$${\color{#9a00c7}{a}}^2$$ `=` $${\color{#00880a}{c}}^2-{\color{#007DDC}{b}}^2$$ Finding a Side $${\color{#9a00c7}{AB}}^2$$ `=` $${\color{#00880a}{18}}^2-{\color{#007DDC}{AB}}^2$$ Plug in the known lengths `AB^2` `+AB^2` `=` `324-AB^2` `+AB^2` Add `AB^2` to both sides `2AB^2` `=` `324` `AB^2-AB^2` cancels out `2AB^2``divide2` `=` `324``divide2` Divide both sides by `2` `2``AB^2``divide2` `=` `162` `times2divide2` cancels out `sqrt(AB^2)` `=` `sqrt162` Take the square root of both sides `AB` `=` `12.73 \text(cm)` Rounded to two decimal places `AB=12.73 \text(cm)`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
All sides of a square are equal, so `a=b=AB`.We can use the Pythagorean Theorem Formula to solve for `AB``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `AB^2``+``AB^2` `=` `18^2` Plug in the known lengths `2AB^2` `=` `324` Evaluate `2AB^2``divide2` `=` `324``divide2` Divide both sides by `2` `2``AB^2``divide2` `=` `162` `times2divide2` cancels out `sqrt(AB^2)` `=` `sqrt162` Take the square root of both sides `AB` `=` `12.73 \text(cm)` Rounded to two decimal places `AB=12.73 \text(cm)` -
Question 2 of 4
2. Question
Find the value of the missing length
The given measurements are in unitsRound your answer to one decimal place- `\text(missing length )=` (10.2)` \text(units)`
Correct
Fantastic!
Incorrect
Method OneFinding a Side
Use $$\large\textbf{-}$$
$${\color{#007DDC}{b}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#9a00c7}{a}}^2$$Labelling each length of the triangle
Use the formula for Finding a Side to solve for `b`$${\color{#007DDC}{b}}^2$$ `=` $${\color{#00880a}{c}}^2-{\color{#9a00c7}{a}}^2$$ Finding a Side $${\color{#007DDC}{b}}^2$$ `=` $${\color{#00880a}{10.6}}^2-{\color{#9a00c7}{2.9}}^2$$ Plug in the known lengths `b^2` `=` `112.36-8.41` Evaluate `b^2` `=` `103.95` `sqrt(b^2)` `=` `sqrt103.95` Take the square root of both sides `b` `=` `10.2 \text(units)` Rounded to one decimal place `b=10.2 \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 `b``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `2.9^2``+``b^2` `=` `10.6^2` Plug in the known lengths `8.41+b^2` `=` `112.36` Evaluate `8.41+b^2` `-8.41` `=` `112.36` `-8.41` Subtract `8.41` from both sides `8.41``+b^2` `-8.41` `=` `103.95` `8.41-8.41` cancels out `sqrt(b^2)` `=` `sqrt103.95` Take the square root of both sides `b` `=` `10.2 \text(units)` Rounded to one decimal place `b=10.2 \text(units)` -
Question 3 of 4
3. Question
The foot of a ladder is `3` metres from the base of a brick wall. If the ladder reaches `7` metres up the wall, find its length.
Round your answer to a whole number- `x=` (8)` \text(m)`
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 `3^2``+``7^2` `=` `x^2` Plug in the known lengths `9+49` `=` `x^2` Evaluate `sqrt(x^2)` `=` `sqrt58` Take the square root of both sides `x` `=` `8 \text(m)` Rounded to the nearest metre `x=8 \text(m)` -
Question 4 of 4
4. Question
Find the value of the missing length `b``a = 23.5` `b=?` `c=32.4`The given measurements are in unitsRound your answer to one decimal place- `b=` (22.3)` \text(units)`
Correct
Excellent!
Incorrect
Method OneFinding a Side
Use $$\large\textbf{-}$$
$${\color{#007DDC}{b}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#9a00c7}{a}}^2$$Labelling each length of the triangle
`a=23.5``c=32.4`Use the formula for Finding a Side to solve for `b`$${\color{#007DDC}{b}}^2$$ `=` $${\color{#00880a}{c}}^2-{\color{#9a00c7}{a}}^2$$ Finding a Side $${\color{#007DDC}{b}}^2$$ `=` $${\color{#00880a}{32.4}}^2-{\color{#9a00c7}{23.5}}^2$$ Plug in the known lengths `b^2` `=` `1049.76-552.25` Evaluate `b^2` `=` `497.51` `sqrt(b^2)` `=` `sqrt497.51` Take the square root of both sides `b` `=` `22.3 \text(units)` Rounded to one decimal place `b=22.3 \text(units)`Method Two
Pythagoras’ Theorem Formula
`a^2``+``b^2``=``c^2``a` and `b` can be switched as they are both sidesLabelling each length of the triangle
`a=23.5``c=32.4`Use the Pythagorean Theorem Formula to solve for `b``a^2``+``b^2` `=` `c^2` Pythagoras’ Theorem Formula `23.5^2``+``b^2` `=` `32.4^2` Plug in the known lengths `552.25+b^2` `=` `1049.76` Evaluate `552.25+b^2` `-552.25` `=` `1049.76` `-552.25` Subtract `552.25` from both sides `552.25``+b^2` `-552.25` `=` `497.51` `552.25-552.25` cancels out `sqrt(b^2)` `=` `sqrt497.51` Take the square root of both sides `b` `=` `22.3 \text(units)` Rounded to one decimal place `b=22.3 \text(units)`