Q) Can any rational value of x make the new area equal to 220 cm2 ?
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Ans: If by increasing each dimension by x units, the area of the photo is enlarged to 220 cm2, then
(18 + x) (12 + x) = 220
⇒ x2 + 30 x + 216 = 220
⇒ x2 + 30 x – 4 = 0
Now to solve, we need to find root values:
We know that d = b2 – 4ac
= 900 +16 = 916
Since 916 is not a perfect square, therefore we can not have any rational value of x to make the new area equal to 220cm2.
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