Question

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

Answer 1

5.055 m by 13.055 m

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.