Question

Speaker Placement. A stereo receiver is in a corner of a 14​-ft by 48​-ft room. Speaker wire will run under a​ rug, diagonally, to a speaker in the far corner. If 3 feet of slack is required on each​ end, how long a piece of wire should be​ purchased?

Answer 1

56 ft

Step-by-step explanation:

The rectangular room has length 14 ft breadth 48 ft.

A speaker is in the far corner of the room. The couch is in between the speaker and receiver. So, length of wire would be the length of the diagonal with the 3 ft slack at both ends.

From Pythagoras theorem we get

Length²+Breadth²=Hypotenuse²

`14^2+48^2=h^2\\\Rightarrow h=√(14^2+48^2)\\\Rightarrow h=√(2500)\\\Rightarrow h=50\ ft`

Length of diagonal is 50 ft

So, with 3 feet of slack on both ends we get

50+3+3 = 56 ft

Length of wire is 56 ft.