Question

A rectangle has an area measuring 1350 square centimeters. Its length and width are whole numbers of centimeters. What are the possible combinations of length and width? which possibility gives the smallest perimeter?.

Answer 1

The smallest perimeter of the rectangle is of value 150 cm.

Given:

The area of the rectangle, A = 1350 cm²

Calculation:

Let the length of the rectangle be 'x'

      the breadth of the rectangle be 'y'

We know that the area of a rectangle is given as:

A = (x) × (y)  

Applying values in the above equation we get:

xy = 1350 cm²

Factorizing the value of 1350, the possible values of length and breadth of the rectangle is as listed below:

x (cm)         y (cm)

1350      ×       1

675       ×       2

450       ×       3

270       ×       5

225       ×       6

150        ×       9

135        ×       10

90         ×       15

75         ×        18

54         ×        25

50         ×        27

45         ×        30         (least possible value)

Thus, the smallest perimeter of the rectangle can be calculated as:

P = 2 (x + y)

  = 2 (45 + 30)

  = 150 cm

Therefore, the smallest perimeter that the rectangle will have is 150 cm.

Learn more about factorization here:

brainly.com/question/9231261

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