The total area is 170 sq. ft. there is 2 rooms. the area of the rooms are 80 and 90 sq. ft. the width of the 2 rooms have no common factors (except 1) find the dimensions of the floor plan using those clues

The dimensions of the floor plan are 17ft by 10ft.

Step-by-step explanation:

We assume that in a rectangular space, we cut out two rooms, which would each also be rectangles.

Here is a diagram:

        w1                    w2        

|      80        |          90           |   L

|                   |                         |

We can see they have the same lengths but different widths. The question specifies the width must be different numbers (and have no common factors except for 1).

The formula for the area of a rectangle is A = lw.

Area Total = L(w1+w2)

170 = L(w1+w2)

If the two areas are 80 and 90 and have the same length, they must have a common factor which is the length.

Find the common factors for the two numbers: These are possible lengths.

10, 5, 2, 1 are the common factors.

Divide each area by each common factor, which is also the length, to find the two possible widths:

Length                       Width for 80              Width for 90

10                                   8                                  9

5                                   16                                  18

2                                   40                                 45

1                                    80                                 90

Which of these pairs of possible widths can be the widths?

8 and 9? Yes. They have no common factors.

16 and 18? No. They have at least the factor "2" in common

40 and 45? No. They have at least the factor "5" in common

80 and 90? No. They have at least the factor "2" in common

The length is 10 and the entire width if 8+9, which is 17.

Use the total area formula to check if this is right:

Area Total = L(w1+w2)

170 = 10(8+9)

170 = 170

Insert the units into the length and width:

The dimensions are 17ft by 10ft.

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