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Mathematics · 2024 · 5 marks
CBSE 2024 · Region 2 · Set 2 · Q33
If the length of a rectangle is reduced by $\displaystyle 5$ cm and its breadth is increased by $\displaystyle 2$ cm, then the area of the rectangle is reduced by $\displaystyle 80 \mathrm{~cm}^{2}$. However, if we increase the length by $\displaystyle 10$ cm and decrease the breadth by $\displaystyle 5$ cm, its area is increased by $\displaystyle 50 \mathrm{~cm}^{2}$. Find the length and breadth of the rectangle.
Marking-scheme solution
Let the length of rectangle be x cm and the breadth be y cm
Area of rectangle = xy
\[\begin{aligned}
& (x-5)(y+2)=x y-80 \Rightarrow 2 x-5 y+70=0 \\
& (x+10)(y-5)=x y+50 \Rightarrow-5 x+10 y-100=0
\end{aligned}
\]
Solving the two equations, we get
\[\begin{aligned}
& x=40 \text { and } y=30 \\
& \therefore \text { Length of rectangle }=40 \mathrm{~cm} \\
& \text { and Breadth of rectangle }=30 \mathrm{~cm}
\end{aligned}
\]
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