Answer
Length of hose is \[13\text{ feet}\].
Work Step by Step
The length and breadth of a rectangular garden are 12 feet and 5 feet respectively. A water faucet is on the one corner of the rectangular garden and a hose is connected to it. Also, length of hose should be enough to reach the opposite corner of the rectangular garden.
Since all the angles of a rectangle intersect each other at\[{{90}^{\circ }}\], therefore, the angle formed at every corner is\[{{90}^{\circ }}\].
The distance between the water faucet and the hose is the hypotenuse whereas the base and perpendicular are length and breadth respectively intersecting each other at\[{{90}^{\circ }}\].
Let base (length) be\[a\]and perpendicular (breadth) be\[b\]. The distance between the water faucet and the hose be\[c\].
Hence,\[a=12\]and\[b=5\].
Compute the value of \[c\]by using Pythagorean Theorem and by using formula
\[\begin{align}
& {{c}^{2}}={{a}^{2}}+{{b}^{2}} \\
& {{x}^{2}}={{12}^{2}}+{{5}^{2}}
\end{align}\]
Now if\[{{12}^{2}}=12.12=144\]and\[{{5}^{2}}=5.5=25\]then solve for c using the equation as shown below.
\[\begin{align}
& {{c}^{2}}=144+25 \\
& {{c}^{2}}=169 \\
& c=\sqrt{169} \\
& c=13
\end{align}\]
Hence, the length of hose is\[13\text{ feet}\].
