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? A) 3 feet B) 7 feet C) 13 feet D) 17 feet

Answer 1

When you draw a diagonal between two vertices of a rectangle, two triangles are formed. So to find the length of the diagonal, find the hypotenuse of one of the triangles:

a^2 + b^2 = c^2

8^2 + 15^2 = c^2

64 + 225 = c^2

c^2 = 289

c = 17 feet (option D)

Answer 2

The Pythagorean Theorem states that: "the sum of the squares of the legs is equal to the square of the hypotenuse."
a² + b² = c²
Note¹: Hypotenuse is the side opposite the right angle.
Note²: The legs are the sides that are not opposite the right angle.


Data:
wide (a) = 8
long (b) = 15
diagonal (c) = ?

Solving:

a² + b² = c²
8² + 15² = c²
64 + 225 = c²
289 = c²
c² = 289

`c = √(289)`

`\boxed{\boxed{c = 17\:feet}}\end{array}}\qquad\quad\checkmark`

Answer:

`\underline{\underline{D)\:17\:feet}}`