Question

While designing the school year book, a teacher told the student that the length and width of a particular photo is increased by x units each to double its area. The original photo is 18 cm long and 12 cm wide.

 Based on the above information, answer the following questions.

1. Write an algebraic equation depicting the above information. 
2. Write the corresponding quadratic equation in standard form. 
3. What should be the new dimensions of the enlarged photo? 
4. Can any rational value of x make the new area equal to 220 cm²?

Answer 1

i. \[(18+x)(12+x)=2(18\times 12)\] 

ii. \[x^{2}+30x-216=0\] 

iiii. Factorising: \[(x+36)(x-6)=0\] so x = 6 (length and width cannot be negative).

New dimensions = 24 cm × 18 cm. 

iv. No. Setting \[(18+x)(12+x)=220\]

\[\Rightarrow x^{2}+30x-4=0\] 

Discriminant \[30^{2}+16=916\] is not a perfect square, so no rational x exists.