Q) 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 double the area of the photo. The original photo is 18 cm long and 12 cm wide.
Based on the above information, answer the following questions:
(I) Write an algebraic equation depicting the above information.
(IT) Write the corresponding quadratic equation in standard form.
(III) What should be the new dimensions of the enlarged photo?
Ans:
Original area of Photo A = 18 x 12 cm2
Its given that by increasing each dimension by x units, area get doubled.
Hence (18 + x) (12 + x) = 2 x (18 x 12) ……………. (i)
⇒ x2 + 30 x + 216 = 2 x 216
⇒ x2 + 30x -216 = 0………………………………………..(ii)
By solving the above equation, we get
(x+36) (x-6) = 0
⇒ x = -36, x = 6
Since x ≠ -36, therefore x = 6
New dimensions of photo are 18+6 and 12+6 i.e. 24 cm & 18 cm