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The length and width of a rectangular plot are in the ratio $5: 3 .$ If the perimeter is $1024 \mathrm{m}$. Find the area.

Last updated date: 13th Jun 2024
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Hint: In geometry, the area can be defined as the space occupied by a flat shape or the surface of an object. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units such as square centimetres, square feet, square inches, etc. A perimeter is a path that encompasses/surrounds a two-dimensional shape. The term may be used either for the path, or its length—in one dimension. It can be thought of as the length of the outline of a shape.

Complete step-by-step answer:
 Perimeter for a 2-dimensional shape is the total distance around the respective shape. For the figures with straight sides such as triangle, rectangle, square or a polygon, the perimeter is the sum of lengths for all the sides.
The area for a 2-dimensional shape is the space enclosed within the perimeter of the given shape. To calculate the area for different shapes, use different formulas based on the number of sides and other characteristics such as angles between the sides.
 Let the length and breadth be $5 \mathrm{x}$ and $3 \mathrm{x}$ $\Rightarrow 2(5 x+3 x)=1024$
$\Rightarrow 16 x=1024$
$\Rightarrow \mathrm{x}=\dfrac{1024}{16}=64$
$\therefore$ Length $=64 \times 5=320 \mathrm{m}$
and breadth $=64 \times 3=192 \mathrm{m}$
area =length $\times$ breadth $=320 \times 192 \mathrm{m}^{2}=6144 \mathrm{m}^{2}$
Therefore, the area is $=320 \times 192 \mathrm{m}^{2}=6144 \mathrm{m}^{2}$.

Note: The concepts of area and perimeter are the basis for understanding Euclidean geometry and calculating the volume of solid shapes in 3-dimensional space such as cones, prism, sphere, and cylinder. Also, we use these formulas for calculating the area and perimeter for quadrilaterals and polygons consisting of sides and curves. The real-life utility of the concept is in several fields such as mapping, architecture, and surveying. The geometric representation of figures is done by sketching the distances and areas for clear understanding.