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horrorfan [7]
3 years ago
14

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

Mathematics
2 answers:
iragen [17]3 years ago
7 0

{15}^{2}  \times  {8 }^{2}  = 289 \\  \\  \sqrt{289 }  = 17
Shkiper50 [21]3 years ago
6 0

Answer:

The path is 17 ft long.

Step-by-step explanation:

Let <em>c</em> represent the length of the hypotenuse of a right triangle, and let <em>a</em> and <em>b</em> 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.

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