Question

A rectangular hall of semicircular voice to type of change the dimensions of the rectangular portion are

Answer 1

Perimeter is a one-dimensional measurement. It is one way to measure the size of something. Formulae abound, but for triangles and quadrilaterals they are so straight-forward as to be rather trivial. The more sides there are of equal length, the simpler the formula. Thus for squares with four equal sides of length s, the perimeter is equal to 4s. In fact, for any regular n-gon with sides of length s the perimeter is equal to ns. For rectangles or kites which have only two different side lengths, say xand y, the perimeter is equal to 2x + 2y. Often the sides of a rectangle are referred to as its length and width.

The word parameter is so often interchanged with perimeter that we shall compare and contrast them here. Parameter: an arbitrary constant each of whose values characterize a member of a system [as a family of curves]. Thus we see perimeter can be one parameter describing a circle, hence much of the confusion. Recall that we also used the word parameter in conjuction with statistics and population.

Consider how you might measure the perimeter of an irregularlly shaped object, say, a kidney shaped swimming pool.

Answer: Possibly lay a rope along the perimeter and then measure the length of the rope. Hopefully, this will be a good enough approximation. If not, solving such problems is one of the reasons calculus was invented!

Irregularly shaped regions can have very large perimeters relative to their area. In fact, rectangles with an area of 100 units2can vary in perimeter from as small as 40 units (each side of 10 units) to virtually infinite, if its length is virtually infinite and its width is infintesimal. What is, for example, the perimeter of a rectangle with width 0.01 units and area 100 square units?

Answer: Since A = lw (see below) and A = 100 and w = 0.01 are given, 100 = l×0.01. Dividing both sides by 0.01 (and applying symmetry) gives l = 10000. Thus the perimeter is 20000.02 units. Note the casual dropping of units during calculation, but specification of units in the end. You will generally get away with this in geometry, but in chemistry and physics specifying units and properly converting between them will be very helpful in solving problems.

While we are on the topic of units, now is a good time to stress some important information. Specifying units is very important in science. Wrong assumptions about units can be very costly. See these write ups about the 1/8 billion dollar MarsOrbiter in Sep. 1999. In fact, recent discoveries have lead to the conclusion that inconsistant units, (Inv. & Tech., Spring 2003, page 11) not only the weather, was an important factor in the English defeat of the Spanish Armada in 1588. We will start earnestly deducting points if units are omitted (or wrong). The world and science uses MKS or SI (metric) whereas most American citizens commonly think in English units. How and when this will change is a good subject for debate!Numbers Lesson 9 provided many useful conversions, especially noting useful ones between the two systems.
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