Q) Can any rational value of x make the new area equal to 220cm² ?

Ans: If by increasing each dimension by x units, the area of photo is enlarged to 220 cm², then

(18 + x) (12 + x) = 220

⇒ x² + 30 x + 216 = 220

⇒ x² + 30 x – 4 = 0

Now, for solving, we need to find root values:

We know that d = b² – 4ac

= 900 +16

= 916

Since 916 is not a perfect square, therefor we can not have any rational value of x to make the new area equal to 220cm².