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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 1 · Set 2 · Q37
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 ?
OR Can any rational value of $\displaystyle x$ make the new area equal to $\displaystyle 220 \mathrm{~cm}^{2}$ ?
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 ?
OR 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 × $\displaystyle 18$ cm
OR
(iii) If \(\displaystyle (18+\mathrm{x})(12+\mathrm{x})=220\)
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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