QuestionA rectangular garden bed measures 16 feet by 12 feet. A water faucet is located at one corner of the garden bed. A hose will be connected to the water faucet. The hose must be long enough to reach the opposite comer of the garden bed when stretched straight. Find the required length of hose.
The required length of the hose is
(Type an exact answer using radicals as needed.)
Studdy Solution
STEP 1
What is this asking?
How long does a hose need to be to reach from one corner of a 16-foot by 12-foot rectangular garden to the opposite corner?
Watch out!
Don't just add the two sides!
We need the diagonal, not the sum of two sides.
STEP 2
1. Draw a Diagram
2. Apply the Pythagorean Theorem
3. Calculate the Length
STEP 3
Let's **visualize** this!
Imagine our garden is a rectangle.
It's long and wide.
We want to find the length of the diagonal – that's the distance from one corner to the opposite corner.
STEP 4
Notice that the diagonal divides the rectangle into two **right triangles**.
This is key because we can use the **Pythagorean Theorem**!
STEP 5
Remember,
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