Please show me how to work this.

A park has two walking paths shaped like right triangles. The first path has legs 75 yd and 100 yd long. the second path has legs 50 yd and 240 yd long. What is the total length of the shorter path, in yards?

the length of each path is the combined length of its legs and its hypotenuse.

As you will recall from your study of the Pythagorean Theorem, the hypotenuse is found using

h^2 = a^2+b^2 where a and b are the legs of the triangle.

1. 75+100+125 = 300
2. 50+250+255 = 555

now, what is the length of the shorter path?

300 yards. I had on the numbers, but did not know to add them. Thanks, again.

To find the total length of the shorter path, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

Let's calculate the length of the hypotenuse for each path:

For the first path:
Using the Pythagorean theorem, the length of the hypotenuse can be found by taking the square root of the sum of the squares of the two legs:
First Path: Hypotenuse = √(75^2 + 100^2)
First Path: Hypotenuse = √(5625 + 10000)
First Path: Hypotenuse = √(15625)
First Path: Hypotenuse ≈ 125

For the second path:
Using the same approach:
Second Path: Hypotenuse = √(50^2 + 240^2)
Second Path: Hypotenuse = √(2500 + 57600)
Second Path: Hypotenuse = √(60100)
Second Path: Hypotenuse ≈ 245

Now, to find the total length of the shorter path, you would add the lengths of the two legs for each path and then choose the shorter path:

First Path: Total length of the shorter path = 75 + 100 = 175 yards
Second Path: Total length of the shorter path = 50 + 240 = 290 yards

Therefore, the total length of the shorter path is 175 yards.

To find the total length of the shorter path, we need to determine the length of each path and then add them together. Let's start with the first path.

The first path is a right triangle with legs measuring 75 yards and 100 yards. To find the length of the hypotenuse (the walking path), we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the legs.

Using the formula c^2 = a^2 + b^2, where c represents the hypotenuse and a and b represent the legs, we can calculate the length of the first path as follows:

c^2 = 75^2 + 100^2
c^2 = 5625 + 10000
c^2 = 15625

To find the length of the hypotenuse, we need to take the square root of 15625:

c = √15625
c ≈ 125 yards

So, the first path has a length of approximately 125 yards.

Next, let's calculate the length of the second path.

The second path is also a right triangle with legs measuring 50 yards and 240 yards. Following the same steps as before, we can use the Pythagorean theorem to determine the length of the second path:

c^2 = 50^2 + 240^2
c^2 = 2500 + 57600
c^2 = 60100

Taking the square root of 60100, we find:

c = √60100
c ≈ 245 yards

Therefore, the second path has a length of approximately 245 yards.

Now, we can find the total length of the shorter path by adding the lengths of the two paths:

Total length of the shorter path = 125 yards + 245 yards
Total length of the shorter path ≈ 370 yards

Thus, the total length of the shorter path is approximately 370 yards.