Let the width be x cm. Then the length is 2x plus 3 cm. Using the perimeter formula gives 2 multiplied by length plus width equals 24. Solving gives width 3 cm and length 9 cm.
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Let the shorter piece be x feet. Then the longer piece is 4x feet. Their total length is 300 feet. Solving 5x equals 300 gives x equal to 60. Therefore, the two pieces are 60 feet and 240 feet.
Let the integers be 2x and 5x because their ratio is 2:5. Their difference is 63. Therefore, 5x minus 2x equals 63. Solving gives x equal to 21. Hence, the integers are 42 and 105.
Let the smaller number be x. Then the larger number is x plus 10. Their sum is 64. Solving the equation gives x equal to 27. Therefore, the two numbers are 27 and 37.
The perimeters are 4 cm, 6 cm, 8 cm, 10 cm and 12 cm respectively. When the side increases by 0.5 cm, the perimeter increases by 2 cm each time. This shows a linear pattern.