The given example of a room is a rectangular prism. Let's look at the room on the given diagram!
We measured a sample room with a similar shape to the diagram. Our sample room had a length of 16 feet, width of 12 feet, and height of 8 feet. When you measure your room, remember that you will probably have different measurements because this is just one of many possible room sizes. Let's add the sample measurements to the diagram.
We will start by calculating the distance from B to C and then we will find the distance from A to B.
Distance from B to C
Notice that the distance from B to C is the length of the diagonal of the rectangular floor in the room. The diagonal divides the floor into two right triangles, with the diagonal as the hypotenuse. This means that we can use the Pythagorean Theorem to find the distance from B to C.
a^2+b^2=c^2
In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We will label a, b, and c.
We can see that a is 12 feet and b is 16 feet. Let's substitute these values into the formula.
The distance from A to B is the length of the diagonal of the room. We can see that the diagonal of the floor, the height of the room, and the diagonal of the room create the right triangle △ ABC. The side connecting A and B is the hypotenuse of the triangle. Again we can use the Pythagorean Theorem to find the distance from A to B.
a^2+b^2=c^2
Let's identify the legs a and b, and the hypotenuse c on △ ABC.
This time we have that a is 8 feet and b is 20 feet. Let's substitute these values into the formula.
