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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.

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 $=320 \times 192 \mathrm{m}^{2}=6144 \mathrm{m}^{2}$.