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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)`