Pythagoras Theorem Mixed Review 1

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Question 1 of 4

Find the value of the missing length

c

$c$

The given measurements are in units

$c =$ $c=$ (5) $units$ $\text(units)$

Question 2 of 4

Find the value of the missing length

k

$k$

The given measurements are in units

$k =$ $k=$ (9) $units$ $\text(units)$

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Method One

Finding a Side

Use $\large\textbf{-}$

a^{2} = c^{2} - b^{2}

${\color{#9a00c7}{a}}^2={\color{#00880a}{c}}^2 \hspace{1mm} \large\textbf{-} \hspace{1mm} \normalsize{\color{#007DDC}{b}}^2$

Use the formula for Finding a Side to solve for $k$ $k$

${\color{#9a00c7}{a}}^2$	$=$ $=$	${\color{#00880a}{c}}^2-{\color{#007DDC}{b}}^2$	Finding a Side
${\color{#9a00c7}{k}}^2$	$=$ $=$	${\color{#00880a}{15}}^2-{\color{#007DDC}{12}}^2$	Plug in the known lengths
$k^{2}$ $k^2$	$=$ $=$	$225 - 144$ $225-144$	Evaluate
$k^{2}$ $k^2$	$=$ $=$	$81$ $81$
$\sqrt{k^{2}}$ $sqrt(k^2)$	$=$ $=$	$\sqrt{81}$ $sqrt81$	Take the square root of both sides
$k$ $k$	$=$ $=$	$9 units$ $9 \text(units)$

k = 9 units

$k=9 \text(units)$

Method Two

Pythagoras’ Theorem Formula

$a^{2}$ $a^2$

+

$+$ $b^{2}$ $b^2$

=

$=$ $c^{2}$ $c^2$

a

$a$ and

b

$b$ can be switched as they are both sides

Labelling each length of the triangle

Use the Pythagorean Theorem Formula to solve for $k$ $k$

$a^{2}$ $a^2$ $+$ $+$ $b^{2}$ $b^2$	$=$ $=$	$c^{2}$ $c^2$	Pythagoras’ Theorem Formula
$k^{2}$ $k^2$ $+$ $+$ $12^{2}$ $12^2$	$=$ $=$	$15^{2}$ $15^2$	Plug in the known lengths
$k^{2} + 144$ $k^2+144$	$=$ $=$	$225$ $225$	Evaluate
$k^{2} + 144$ $k^2+144$ $- 144$ $-144$	$=$ $=$	$225$ $225$ $- 144$ $-144$	Subtract $144$ $144$ from both sides
$k^{2}$ $k^2$ $+ 144$ $+144$ $- 144$ $-144$	$=$ $=$	$81$ $81$	$144 - 144$ $144-144$ cancels out
$\sqrt{k^{2}}$ $sqrt(k^2)$	$=$ $=$	$\sqrt{81}$ $sqrt81$	Take the square root of both sides
$k$ $k$	$=$ $=$	$9 units$ $9 \text(units)$

k = 9 units

$k=9 \text(units)$

Question 3 of 4

Find the value of the missing length

x

$x$

Round your answer to 2 decimal places

$x =$ $x=$ (11.66) $cm$ $\text(cm)$

Question 4 of 4

Find the value of the missing length

y

$y$

Round your answer to 2 decimal places

$y =$ $y=$ (14.42) $cm$ $\text(cm)$

Pythagoras Theorem Mixed Review 1

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Quiz summary

Information

1. Question

Hint

Well Done!

Pythagoras’ Theorem Formula

Labelling each length of the triangle

2. Question

Hint

Great Work!

Finding a Side

Use $\large\textbf{-}$

Pythagoras’ Theorem Formula

Labelling each length of the triangle

3. Question

Hint

Nice Job!

Pythagoras’ Theorem Formula

Labelling each length of the triangle

4. Question

Hint

Excellent!

Pythagoras’ Theorem Formula

Labelling each length of the triangle

Quizzes

Pythagoras Theorem Mixed Review 1

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Well Done!

Pythagoras’ Theorem Formula

Labelling each length of the triangle

2. Question

Hint

Great Work!

Finding a Side

Use --\large\textbf{-}

Pythagoras’ Theorem Formula

Labelling each length of the triangle

3. Question

Hint

Nice Job!

Pythagoras’ Theorem Formula

Labelling each length of the triangle

4. Question

Hint

Excellent!

Pythagoras’ Theorem Formula

Labelling each length of the triangle

Quizzes

Use $\large\textbf{-}$