Question

A rectangular garden is 8 feet wide and 15 feet long. A diagonal path cuts through the entire garden. How long is the path?

Answer 1

${15}^{2} \times {8 }^{2} = 289 \\ \\ \sqrt{289 } = 17$

Answer 2

Answer:

The path is 17 ft long.

Step-by-step explanation:

Let c represent the length of the hypotenuse of a right triangle, and let a and b represent the lengths of its legs, as pictured in the image below.

The relationship involving the legs and hypotenuse of the right triangle, given by

$a^2+b^2=c^2$

is called the Pythagorean Theorem.

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 8 feet wide and 15 feet long.

Applying the Pythagoras' Theorem, we get

$d^2=(8)^2+(15)^2\\d^2=64+225\\d^2=289\\d=\sqrt{289}=17$

Technically, there are two answers to $d^2=289$, i.e., d = 17 or d = -17. However, d represents the hypotenuse of the right triangle and must be non-negative. Hence, we must choose d = 17.

The path is 17 ft long.