P= 16cm

a=6 cm

We know that, perimeter of any given figure is its sum of sides that is

a+b+c= 16

6 + b + c= 16

b + c= 10

Let us consider b=x, then c= 10-x.

S= (a+ b+ c)/2 = 8.  

A= Sq. rt of {s(s-a)(s-b)(s-c)}

A²= {8(8-6) (8-x) (8-(10-x)}

A² = 16 (8-x) (x-2) = 16 (8x-x² -16 +2x)

A² = 16 (10x- x² -16)

dA²/ dx = 16 (10-2x) dA² /dx = 0. (for maximum area)

x = 5.

Therefore, b= 5 cm

c= 10-5 = 5 cm.

Ans: The other two sides are 5 cm and 5cm so that the area of the triangle is maximum.

Perimeter can be defined as the path which mainly surrounds the given two dimensional shape. The term is need for the path or mainly for its length for one dimension. It is considered to be as the length of outline for any given shape. Perimeter of given shape that is circle or ellipse can be defined as the circumference. All the calculation with respect to several practical applications which is perimeter of the length of fence needed by the yard. Perimeter for a given wheel describes that how it can roll in one revolution. Amount of string aims to spool in the perimeter for the length for the string which is exactly which is equal in perimeter.

Polygons are completely fundamental which is needed for analysing the perimeter not because of the fact that they are simple shape. It is mainly calculated by approximation of sequences for polygons which trend the shapes. Archimedes is known to be the first mathematician which is mainly used for reasoning purpose. The approximated perimeter of any given circle is surrounded by help of regular polygons. Perimeter of the polygon is found to be equal to the sum of its sides. More specifically, the perimeter of a rectangle of width w a length l the value stands to be 2w+ 2l.

In case of equilateral polygon, the polygon comes up with side which is of same length. Rhombus comes up with 4 –sided equilateral polygon. The perimeter of equilateral polygon can be calculated by multiplying the common length of sides of number of sides. In general, a regular polygon comes up with sides and by its circumradius. There is a constant distance in between the centre and vertices. Length of its can be calculated by the help of trigonometry. Splitter of a given triangle aims to divide the perimeter into two equal parts which are defined as the semiperimetre of the triangle. Three splitters of a given triangle aim to intersect with each other at the Nagel of the triangle. Cleaver of the triangle can be defined as a segment for midpoint for side of the triangle to the opposite side. This is done in such a way that it can divide the perimeter into equal lengths. When three cleavers of a given triangle intersect with each other then it is defined as Spieker centre.

Perimeter of a given circle is often defined as the circumference. It is completely proportional to the diameter and radius. Perimeter and area are considered to main measures of geometric figures. There is some confusion in between them which is common error that believes greater for any of them. Commonplace observation is defined as reduction which a shape in the marketplace for grow area along with perimeter.  

Area can be defined as the quantity that highlights the extent of two-dimensional figures and shapes in plane. Surface area can be defined as an analog of two-dimension surface and three-dimension object. Area is completely understood by the value of material in the provided thickness which is needed for fashion for model of the shape. It can be defined as the amount of paint which is needed for covering a surface by the help of simple coat. It can be defined as two-dimensional along for the length of the curve or even volume of the solid.

The area of the given shape can be measured by comparison of the shapes with the squares based on fixed size. In SI unit, the standard unit of area is found to be square meter which is the area for the square whose side is single meter long. The shape area of three squares come up with same area like the square. In unit square, area of any given shape is defined as dimensionless real number. There are different kind of formula for area which is based on shapes like triangle, circle and rectangle. By the help of this formula, the area of polygon can be calculated by dividing the polygon in the form of a triangle. There are many shapes that have curved boundary where calculus is needed for calculating the area of the figure which have motivation in the historical calculus development.

For some of the solid figures like cone and cylinder the overall area of boundary surface can be defined as surface area. There are many formulas which are based on the surface area of simple shapes which is calculated by ancient Greeks. Calculation based on surface area tends to have much more complicated shape that requires multivariable calculus. Area aims to play a key role in present day mathematics. Along with this, it is important in geometry and calculus that area is completely related to determinants in algebra. This can be defined as the basic property of surface which is needed in differential geometry. By using of Lebesgue measure, the area of a subset of the plane is completely defined although each and every subset is not measured. Area can be stated as the use of axioms which is again defined as the collection of particular plane which figures to be set of real numbers. This mere acts like a function which exits. Area can be defined as the function of collection of M for special plane figures to the set of real numbers that satisfies some specific properties.