8. CBQ - Quadratic equation

Question:

4 m.

A teacher, while designing the school yearbook, told a student to increase both the length and width of a rectangular photograph by \(x\ cm\) each so that its area becomes double the original area. If the original dimensions of the photo are \(18\ cm \times 12\ cm\).

Based on the above information, answer the following questions:

(i) Frame an algebraic equation using the above information.

\((x + 18) (x + 12) = 2 (18 \times 12)\)
\((x - 18) (x + 12) = 2(18 \times 12)\)
\((x + 18)( x - 12) = (18 \times 12)\)
\((x + 18) (x + 12) = (18 \times 12)\)

(ii) Write the corresponding quadratic equation in standard form.

\(x^2 - 30x - 216 = 0\)
\(x^2 + 30x - 216 = 0\)
\(x^2 - 36x +216 =0\)
\(x^2 + 216x - 324 = 0\)

(iii) After increasing both the length and width by \(x\ cm\), what are the new dimensions of the photograph?

Length \(=24\ cm\), Width \(=18\ cm\)
Length \(=24\ cm \), Width \(=16\ cm\)
Length \(=36\ cm\), Widht \(=18\ cm\)
Length \(=18\ cm\), Width \(= 22\ cm\)

(iv) Can any rational value of \(x\) make the new area equal to \(220 \ cm^2\)?

No
Yes

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