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