To get from his high school to his home, Jamal travels 5.0 miles east and then 4.0 miles north. When Shelia goes to her home from the same high school she travels 8.0 miles east and 2.0 miles south. What is the measure of the shortest distance, to the nearest tenth of a mile, between Jamals home and Shelias home?

I don't understand how to figure this one out!?

draw a diagram to find that the result is 2 similar triangles. one side of the bigger triangle is 4, and the same side of the smaller triangle is 2, so there is a 2 to 1 ratio between the triangles. you know that the bottoms of both triangles add up to 3. if there is a 2 to 1 ratio, the larger triangle's side is 2 and the smaller triangle's side is 1. use pythagorean theorem to find the hypotenuse of both triangles, (5 and root 5) and add them together

To find the shortest distance between Jamal's home and Sheila's home, we can use the Pythagorean theorem.

Step 1: Draw a diagram to represent the paths taken by Jamal and Sheila. The diagram will show two right triangles, with one side measuring 5.0 miles and the other side measuring 4.0 miles for Jamal, and one side measuring 8.0 miles and the other side measuring 2.0 miles for Sheila.

Step 2: Notice that the smaller triangle formed by Sheila's path is a scaled-down version of the larger triangle formed by Jamal's path. The ratio between the sides of the two triangles is 2 to 1.

Step 3: Since the bottom sides of both triangles add up to 3.0 miles (4.0 miles - 1.0 mile), and the ratio is 2 to 1, Sheila's triangle has a bottom side length of 1.0 mile.

Step 4: Use the Pythagorean theorem to find the hypotenuse of both triangles. For Jamal's triangle, the hypotenuse is √(5.0^2 + 4.0^2) = √(25 + 16) = √41 miles. For Sheila's triangle, the hypotenuse is √(8.0^2 + 2.0^2) = √(64 + 4) = √68 miles.

Step 5: Add the lengths of the two hypotenuses to find the shortest distance between the two homes. √41 miles + √68 miles ≈ 6.4 miles (rounded to the nearest tenth of a mile).

Therefore, the measure of the shortest distance between Jamal's home and Sheila's home is approximately 6.4 miles.

To solve this problem, we can use the Pythagorean Theorem and some basic geometry concepts.

First, let's draw a diagram to visualize the situation. We can label the distances traveled by Jamal and Shelia as follows:

Jamal: 5.0 miles east and 4.0 miles north
Shelia: 8.0 miles east and 2.0 miles south

Now, let's label the points on the diagram. Let's say Jamal's home is point A and Shelia's home is point B.

To find the shortest distance between Jamal's home and Shelia's home, we need to find the length of the line segment AB.

Looking at the diagram, we can see that the triangle formed by the line segments AB, BC, and AC is a right triangle. This is because AC (5.0 miles) is parallel to the x-axis and BC (4.0 miles) is parallel to the y-axis.

Since we have a right triangle, we 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 other two sides.

Let's apply this theorem to our problem. The length of the hypotenuse AB is what we want to find.

Using the Pythagorean Theorem, we can write the following equation:

AB^2 = AC^2 + BC^2

Substituting the values:

AB^2 = (5.0 miles)^2 + (4.0 miles)^2
AB^2 = 25.0 miles^2 + 16.0 miles^2
AB^2 = 41.0 miles^2

Now, to find the shortest distance between Jamal's home and Shelia's home, we need to take the square root of both sides:

AB = √(41.0 miles^2)

Calculating the square root using a calculator or approximating, we find that AB is approximately equal to 6.4 miles to the nearest tenth of a mile.

Meh