Joel is laying pipe for a sprinkler system before he plants his lawn.The lawn is a rectangle 15 feet long and 8 ft wide. He needs to lay a piece if pipe that will run diagonal along the lawn. It will divide the area of the lawn into two right triangles. what will be the length of that diagonal piece of pipe?
Ahh -- time for the Pythagorean Theorem.
a^2 + b^2 = c^2
15^2 + 8^2 = c^2
225 + 64 = c^2
289 = c^2
17 = c
To find the length of the diagonal piece of pipe, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length of one side of the rectangle is 15 feet, and the width is 8 feet. So, one side of the right triangle formed by the diagonal pipe will be 15 feet, and the other side will be 8 feet.
Let's label the length of the diagonal pipe as 'd', the side length of 15 feet as 'a', and the side length of 8 feet as 'b'.
According to the Pythagorean theorem, we have:
d^2 = a^2 + b^2
Substituting the given values, we get:
d^2 = 15^2 + 8^2
d^2 = 225 + 64
d^2 = 289
Now, to find the length of 'd', we take the square root of both sides:
√(d^2) = √289
d = √289
d = 17
Therefore, the length of the diagonal piece of pipe will be 17 feet.
To find the length of the diagonal piece of pipe, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right triangles are the length (15 feet) and the width (8 feet) of the lawn, and the hypotenuse is the diagonal piece of pipe we're trying to find.
Therefore, we can calculate the length of the diagonal piece of pipe as follows:
Step 1: Square the length and the width of the lawn.
15^2 = 225
8^2 = 64
Step 2: Add the two results together.
225 + 64 = 289
Step 3: Take the square root of the sum to find the length of the diagonal piece of pipe.
√289 = 17
Therefore, the length of the diagonal piece of pipe is 17 feet.