10. CBQ - Quadratic equation

Question:

4 m.

In a school yearbook project, a photo measuring \(18\ cm\) in length and \(12\ cm\) in width has to be enlarged such that both its length and width increase by \(x\ cm\) and its area becomes twice the original.

Based on the above information, answer the following questions:

(i) Write an algebraic equation depiciting the above information.

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

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

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

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

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

Yes
No

Login or Fast registration

Previous task

Exit to the topic

Next topic

Send feedback

Did you find an error?

Send it to us!