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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