Solution:
Let the length and breadth of the rectangle be x units and y units respectively.
Hence, the area of rectangle = xy sq.units
Length is increased by 7 m
⇒ now, the new length is
![\[x+7\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-07b4e8c4b5a87deead93b06b99d830de_l3.png "Rendered by QuickLaTeX.com")
Breadth is decreased by 3 m
⇒ now, the new breadth is
![\[y-3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c55cf748986fac420c92b116006e3bb8_l3.png "Rendered by QuickLaTeX.com")
The area of the rectangle = xy.
Calculation,
![\[xy\text{ }=\text{ }\left( x+7 \right)\left( y-3 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ae3ecd137b1b18d481bb70665c37be5e_l3.png "Rendered by QuickLaTeX.com")
![\[xy\text{ }=\text{ }xy\text{ }+\text{ }7y\text{ }-\text{ }3x\text{ }-\text{ }21\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-69b8459db16feb3b8157a3ab505b9725_l3.png "Rendered by QuickLaTeX.com")
![\[3x\text{ }\text{ }7y\text{ }+\text{ }21\text{ }=\text{ }0\text{ }\ldots \ldots \ldots .\text{ }\left( i \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d89f0544f3f465422df9ebb43fade3ae_l3.png "Rendered by QuickLaTeX.com")
Length is decreased by 7 m
⇒ The new length is
![\[x-7\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c11a7aca012cabc1fd6b487f63871740_l3.png "Rendered by QuickLaTeX.com")
Breadth is increased by 5 m
⇒ The new breadth is
![\[y+5\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f007d0bff779262e924902f7e59b0be_l3.png "Rendered by QuickLaTeX.com")
The area of the rectangle = xy.
Calculation,
![\[xy\text{ }=\text{ }\left( x-7 \right)\left( y+5 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0b3ac469388baa790a510c0c510f3dbf_l3.png "Rendered by QuickLaTeX.com")
![\[xy\text{ }=\text{ }xy\text{ }-\text{ }7y\text{ }+\text{ }5x\text{ }-\text{ }35\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-844f7511139b4294b5b8d83b1cff9ed4_l3.png "Rendered by QuickLaTeX.com")
![\[5x\text{ }\text{ }7y\text{ }\text{ }35\text{ }=\text{ }0\text{ }\ldots \ldots \ldots .\text{ }\left( ii \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c9ff1ed14350a090fbcd41a3addb7cba_l3.png "Rendered by QuickLaTeX.com")
By cross-multiplication method, Solve (i) & (ii),
![\[\frac{x}{\left( -7\times -5 \right)-\left( -7\times 21 \right)}=\frac{y}{\left( -3\times -35 \right)-\left( -5\times 21 \right)}=\frac{1}{\left( 3\times -7 \right)-\left( 5\times -7 \right)}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-46792588764cf8be0333b18d8ce7d052_l3.png "Rendered by QuickLaTeX.com")
![\[\frac{x}{245+147}=\frac{-y}{-105-105}=\frac{1}{-21+35}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-92ea44fabfbbce289850725d011d4879_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }=\text{ }\frac{392}{14}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9dc3cf0d89172a5896579553776b3650_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }=\text{ }28\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5f1f20158805f9265e0efbec72be4111_l3.png "Rendered by QuickLaTeX.com")
And,
![\[y\text{ }=\text{ }15\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5fbbc2f6a5563ea7164ee59436481b00_l3.png "Rendered by QuickLaTeX.com")
The breadth = 15 m.