Question

An auditorium is in the shape of an equilateral triangle. the stage extends from one vertex of the triancle to the midsegment, and the seating area extends from the midsegment to the resr wall. the rear wall measures 112 feet. what is the perimeter of the seating area.

Answer 1

Answer:

280 ft

Step-by-step explanation:

An auditorium is in the shape of an equilateral triangle with side length as 112 ft.

The stage extends from one vertex of the triangle to the mid-segment and the seating area extends from the mid-segment to the rear wall.

*The situation is represented in the attachment.

According to the midpoint theorem, the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.

Hence, the length of the mid-segment in this case is,

$\dfrac{1}{2}\times 112=56\ ft$

Therefore, the perimeter of the seating area is,

$=112+56+56+56=280\ ft$