Resources for Pythagoras Word Problems
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Pythagoras Word Problems Theory
![\begin{multicols}{2} \textbf{Example 1}\\ The perimeter of a square is \(44 \text{~cm}\) Find the length of its diagonal (to 1dp).\\ \textbf{Example 1 solution}\\ \(\begin{aligned} d^2 & =11^2+11^2 \\ & =242 \\ d & =\sqrt{242} \\ & =15.6 \text{~cm}. \end{aligned}\)\\ \begin{center} \begin{tikzpicture}[scale=1] \coordinate[label=below right:] (O) at (0,0); \coordinate[label=above:] (A) at (0,3); \coordinate[label=below left:] (B) at (-3,0); \coordinate[label=above:] (D) at (-3,3); \draw[line width=1pt] (O)--(B)node[midway ,below] {11}--(D)node[left,midway]{11}--(A) node[midway,above] {11}--(O)node[midway ,right] {11}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \draw[line width=1pt] (B)--(A)node[midway ,above left] {\(d\)}; \end{tikzpicture} \end{center} \columnbreak \textbf{Example 2}\\ The area of \(\triangle A B C\) is \(6 \mathrm{~cm}^2\).\\ \textbf{i)} Find \(A B\)\\ \textbf{ii)} Find \(A C\) \begin{center} \begin{tikzpicture}[scale=0.8] \coordinate[label=below right:B] (O) at (0,0); \coordinate[label=above:A] (A) at (0,4); \coordinate[label=below left:C] (B) at (-3,0); \draw[line width=1pt] (O)--(B)node[midway ,below] {3}--(A)node[left=4pt,midway]{}--(O) node[midway,right] {}; \pic [draw=black,line width=1pt,angle radius=0.4cm,angle eccentricity=1.6,""] {right angle=B--O--A}; \end{tikzpicture} \end{center} \textbf{Example 2 solution}\\ \(\begin{aligned} \textbf{i) } &\begin{aligned}[t] \text { Area }&=\frac{1}{2} \times 3 \times A B \\ \frac{3 A B}{2}&=6 \\ 3 AB&=12 \\ AB&=4 \text{~cm} . \end{aligned}\\ \textbf{ii) } &\begin{aligned}[t] A C^2 & =A B^2+B C^2 \\ & =4^2+3^2 \\ A C^2 & =25 \\ A C & =\sqrt{25} \\ A C & =5 \text{~cm} \end{aligned} \end{aligned}\) \end{multicols}](/media/wdeopb3l/9235.png)
NSW Y8 Maths Pythagoras Pythagoras Word Problems
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Pythagoras Word Problems - Video - Pythagoras Word Problems - Example 1
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