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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 1 · Set 1 · Q36
While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x units each to…
While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by $\displaystyle x$ units each to double the area of the photo. The original photo is $\displaystyle 18$ cm long and $\displaystyle 12$ cm wide. Based on the above information, answer the following questions :
(I)
Write an algebraic equation depicting the above information.
(II)
Write the corresponding quadratic equation in standard form.
(III)
What should be the new dimensions of the enlarged photo ?
Can any rational value of $\displaystyle x$ make the new area equal to $\displaystyle 220 \mathrm{~cm}^{2}$ ?
Marking-scheme solution
(i) \(\displaystyle (18+\mathrm{x})(12+\mathrm{x})=2(18 \times 12)\)
(ii) \(\displaystyle \mathrm{x}^{2}+30 \mathrm{x}-216=0\)
(iii) Solving : \(\displaystyle \mathrm{x}^{2}+30 \mathrm{x}-216=0\)
\[\begin{aligned}
\Rightarrow( & x+36)(x-6)=0 \\
& x \neq-36 \therefore \Rightarrow x=6 .
\end{aligned}
\]
new dimensions are $\displaystyle 24$ cm × $\displaystyle 18$ cmIf \(\displaystyle (18+\mathrm{x})(12+\mathrm{x})=220\)
then \(\displaystyle \mathrm{x}^{2}+30 \mathrm{x}-4=0\)
Here \(\displaystyle \mathrm{D}=900+16=916\) which is not a perfect square.
Thus we can't have any such rational value of x.
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CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.