Question

The rectangular room shown 20 feet long, 48 feet wide, and 10 feet tall. Use the Pythagorean Theorem to find the distance from B to C and the distance from A to B . Round to the nearest tenth, if necessary.

Answer 1

Explanation:

We can use the Pythagorean Theorem to find the distances from B to C and from A to B.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's first find the distance from B to C. We can see that the length from B to C is the hypotenuse of a right triangle with legs of length 10 feet and 20 feet. So, using the Pythagorean Theorem, we can write:

distance from B to C = sqrt(10^2 + 20^2)

distance from B to C = sqrt(500)

distance from B to C ≈ 22.36 feet (rounded to the nearest tenth)

Therefore, the distance from B to C is approximately 22.36 feet.

Now, let's find the distance from A to B. We can see that the width of the room, from A to B, is the hypotenuse of a right triangle with legs of length 10 feet and 48 feet. So, using the Pythagorean Theorem, we can write:

distance from A to B = sqrt(10^2 + 48^2)

distance from A to B = sqrt(2354)

distance from A to B ≈ 48.5 feet (rounded to the nearest tenth)

Therefore, the distance from A to B is approximately 48.5 feet.