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Q: A rectangle has a perimeter of 44 the dimensions of the rectangle are scaled by a factor of 1.5 so what will be the perimeter of the resulting figure?

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The length and breadth of a rectangle are a factor pair of the area of the rectangle.

A rectangle 10.5 x 3 will have a perimeter of 27 in.

The perimeter, being a linear measure, also changes by a factor of 3.

(20,5)

The perimeter correspondingly increases by a factor of 4.

18" is not a possible perimeter measurement. Assume the dimensions of the rectangle are so close to those of a square that the difference can be disregarded. This is the condition when the perimeter is at its minimum. When the rectangle measures approximately 6" x 6", its area = 36 sq ins, its perimeter = 24" For the area to remain constant then as the length increases by a factor n the width must decrease by that same factor. Area = 6n x 6/n : perimeter = 12n + 12/n :so when n = 1, Perimeter = 12 + 12 = 24 As n increases, say n = 2, Perimeter = 24 + 6 = 30 : And the perimeter continues to increase as the rectangle becomes narrower. Eventually, it will become so narrow that for diagram purposes it will appear as a straight line.

Perimeter is proportional to the linear dimensions, so it increases by 3x .Area is proportional to (linear dimensions)2, so it increases by 9x .

The ratio of the perimeters is equal to the scale factor. If rectangle #1 has sides L and W, then the perimeter is 2*L1 + 2*W1 = 2*(L1 + W1).If rectangle # 2 is similar to #1 and sides are scaled by a factor S, so that L2 = S*L1 and W2 = S*W1, the perimeter of rectangle #2 is 2*(L2 + W2)= 2*(S*L1 + S*W1) = S*2*(L1 + W1) = S*(perimeter of rectangle #1).

The absolute value of the perimeter doesn't change, only the unit value which increases by a factor of 3.

32 x 1 16 x 2 8 x 4

Scale factor and perimeter are related because if the scale factor is 2, then the perimeter will be doubled. So whatever the scale factor is, that is how many times the perimeter will be enlarged.

The number of square tiles is always equal to factor pairs. As an example, imagine a rectangle that contains 8 squares - 2 rows of 4. 2 X 4 = 8. In other words, the dimensions of the rectangles are ALWAYS equal to a factor pair of the number of squares in the rectangle. A rectangle containing 24 squares could be made as 24x1, 12x2, 8x3, or 6x4.

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