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.