A water faucet is located in one corner of Juan's garden. He wants a garden hose long enough to reach the farthest corner of the garden. The garden is rectangular with sides of 10 feet and 15 feet. How long should the garden hose be? Show your work

Let's find the diagonal length of this rectangle, which is the hypotenuse of a triangle.

a^2 + b^2 = c^2

10^2 + 15^2 = c^2

100 + 225 = c^2

325 = c^2

18.028 = c

Looks like an 18 foot hose will do the job.

A rectangle has a width of 8 meters. The length is twice as long as the width. What is the length of the diagonal? Show your work

To determine the length of the garden hose needed to reach the farthest corner of the rectangular garden, we can use the Pythagorean theorem. Here's how:

1. Start by drawing a diagram of the rectangular garden.

|----------15ft----------|
_______
| |
10ft | |
|_______|

2. The water faucet is located in one corner, and we want to find the length of the garden hose to reach the opposite corner, which is the longest distance.

3. Apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the two shorter sides of the right triangle are the dimensions of the garden: 10ft and 15ft.

Let's denote the length of the garden hose as 'x.' So, we have:

x^2 = 10^2 + 15^2
x^2 = 100 + 225
x^2 = 325

4. To find the value of 'x,' we take the square root of both sides:

√(x^2) = √325
x = √325
x ≈ 18.03 (rounded to two decimal places)

Therefore, the garden hose should be approximately 18.03 feet long to reach the farthest corner of Juan's garden.