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How are the perimeter and area of a rectangle affected if the legth and the width are changed proportionally?
Wiki User
∙ 13y ago
If the length and width of a rectangle are both multiplied by K, then the original
perimeter is multiplied by K, and the area is multiplied by K2 .
Wiki User
∙ 13y ago
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How does proportional change in the dimensions affect the perimeter of a figure?
If you are asking how the perimeter of an object changes if the whole object is proportionally changed: The perimeter changes by the same factor as the change in proportion of the whole object. For example: given a square that is 2 units by 2 units, changed by a factor of four, the new size would be 8 units by 8 units. The original perimeter was 2+2+2+2=8. The new perimeter is 8+8+8+8=32. So, multiplying the original perimeter, 8, by the factor of proportional change, 4, we get 8x4=32. For any object, multiply the original perimeter by the factor of proportional change to arrive at the new perimeter.
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To answer that question, look at the formulas for both Let's take a rectangle with length L and width W. The area is LW and the perimeter is 2L+2W So can LW=2L+2W Solve for L LW/2=L+W 1/2L(w-2)=w L=(2w)/(W-2) This tells us the answer is YES. But it also tells us W must be greater than 2. Try W=3, this gives us L= 6/1=6 So look at a 6x3 rectangle Area is 18 and perimeter is 12+6=18 True, but there is an important caveat. The numbers, for the area and perimeter, can be the same but the two cannot be the same. The simple reason is that the area will be in square units whereas the perimeter will be in linear units. The consequnce of this is that if the units of measurement are changed (eg from centimetres to metres, or inches) the equality in numbers will no longer hold.
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