The rectangular room shown has a length of 20 ft, width of 48 ft, and height of 10 ft. Use the Pythagorean Theorem to find length BC and length AB. Round to the nearest tenth, if necessary.
Answers
Answer: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 =
substituting the values of length and width
⇒ Diagonal =
⇒ Diagonal =
⇒ Diagonal = 52 feet ← distance from B to C
and
The diagonal of the rectangular room is given by,
Diagonal² = Length² + Width² + Height²
⇒ Diagonal =
substituting the values of length, width and height
⇒ Diagonal =
⇒ Diagonal =
⇒ 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.
Step-by-step explanation:
