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

Given:

The length of the room = 20 feet

The width of the room = 48 feet

The height of the room = 10 feet

To find:

(i) The distance from B to C

(ii) The distance from A to B

Formula to be used:

Pythagorean Theorem: Hypotenuse² = Perpendicular² + Base²

Solution:

We know that all the angles of a rectangle is 90°.

So, we will use the Pythagorean Theorem to find the distance from B to C i.e., the length of the diagonal of the floor and the distance from A to B i.e., the length of the diagonal of the room. (as shown in the figure)

Therefore,

The diagonal of the floor of the rectangular room is given by,

Diagonal² = Length² + Width²

⇒ Diagonal = $\sqrt{Length^2\:+\:Width^2}$

substituting the values of length and width

⇒ Diagonal = $\sqrt{20^2\:+\:48^2}$

⇒ Diagonal = $\sqrt{2704}$

⇒ Diagonal = 52 feet ← distance from B to C

and

The diagonal of the rectangular room is given by,

Diagonal² = Length² + Width² + Height²

⇒ Diagonal = $\sqrt{Length^2\:+\:Width^2\:+\:Height^2}$

substituting the values of length, width and height

⇒ Diagonal = $\sqrt{20^2\:+\:48^2\:+\:10^2}$

⇒ Diagonal = $\sqrt{2804}$

⇒ Diagonal = 52.952 feet ≈ 53 feet (rounded to the nearest tenth) ← distance from B to C

Thus, the distance from B to C is 52 feet and the distance from A to B is 53 feet.

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