1. The sides of a right angled triangle consisting the right angle are 5cm and 12cm, find its hypotenus.
\[AC^2=AB^2+BC^2\]
\[=5^2+12^2\]
\[=25+144\]
\[=169\]
\[AC=\sqrt{169}=13 cm\].
2. Find the length of the diagonal of a square of side 12cm.
In \[ \Delta ABC,\] \[A \hat{B} C= {90}^{\circ}\]
\[AC^2=AB^2+BC^2\]
\[=12^2+12^2\]
\[=144+144=2\sqrt{144}\]
\[AC=\sqrt{2\times 144}=12\sqrt{2}cm.\]
3. The length of diagonal of a rectanglar playground is 125m and the length of one side is 75m. Find the length of the other side.
In \[ \Delta ABC,\] \[BC =75m,\] \[AC =125m,\] \[AB=?\]
In \[ \Delta ABC,\] \[A \hat{B} C= {90}^{\circ}\]
\[AB^2+BC^2=AC^2\]
\[AB^2=AC^2-BC^2\]
\[=125^2-75^2\]
\[AB^2=(125+75)(125-75)\] \[a^2-b^2=(a+b)(a-b)\]
\[=200\times 50\]
\[=10,000\]
\[AB=\sqrt{10,000}=100m\]
