3)A 3m by 11m rug covers half of the floor area of a rectangular room. It
leaves a uniform strip of bare floor around the edges. What are the
dimensions of the room? Include a diagram, let statement, equation, full
solution and therefore statement. Round your final answer to 3 decimal
places. Show all work for full marks! TH - 5

  5.055 m by 13.055 m

Step-by-step explanation:

Let x represent the width of the room in meters. Then the length is x+8 meters, and the room area is ...

  A = LW = (x+8)(x) = 2(rug area)

  x^2 +8x = 2(3)(11) = 66

Completing the square, we have ...

  x^2 +8x +16 = 82

  (x +4)^2 = 82

  x = -4 ±√82 ≈ {-13.055, +5.055}

The magnitudes of these dimensions are the dimensions of the room:

  √82 ± 4 = {5.055, 13.055} . . . meters

Therefore, the room is 5.055 × 13.055 meters.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,