Abey Numkena is an interior designer. She has been asked to locate an oriental rug for the new corporate office. As a rule, the rug should cover 1/2 of the total floor area with a uniform width surrounding the rug.
a) If the dimensions of the room are 12 ft by 16 ft, write an equation to model the situation.
b) What are the dimensions of the rug?
If the width surrounding the rug is w, then
(12-2w)(16-2w) = 12*16/2
Now just solve for w and determine the rug dimensions.
To model the situation, we first need to calculate the area of the room and then determine the dimensions of the rug.
a) To find the area of the room, we multiply its length by its width:
Area of the room = length × width
Area of the room = 12 ft × 16 ft
Now, to represent the rug dimensions, let's assume the width of the uniform surrounding area is 'x'.
The length of the rug would be the same as the length of the room (12 ft), as it should cover 1/2 of the total floor area.
The width of the rug would be given by:
Width of the rug = Width of the room - 2 × surrounding area width
Width of the rug = 16 ft - 2 × x ft
Hence, the equation representing the situation would be:
Area of the rug = (Width of the rug) × (Length of the rug)
Area of the rug = (16 ft - 2x ft) × 12 ft
b) To find the dimensions of the rug, we can use the equation above and solve for the variables.
However, since the question asks for the dimensions, we need to assume a value for 'x' (the width of the uniform surrounding area).
For example, let's assume 'x' is 1 ft:
Area of the rug = (16 ft - 2 × 1 ft) × 12 ft
Area of the rug = 14 ft × 12 ft
Area of the rug = 168 ft²
Now, to find the dimensions of the rug, we can divide the area by the length:
Width of the rug = Area of the rug / Length of the rug
Width of the rug = 168 ft² / 12 ft
Width of the rug = 14 ft
Thus, the dimensions of the rug would be 14 ft by 12 ft when the width of the uniform surrounding area is assumed to be 1 ft.