CBSE Class 10 Maths (Standard) 2023 · Paper 30/1/1 · Question 36

Quadratic Equations 4 marks Medium

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 :

Original photo enlarged by x on each dimension

IWrite an algebraic equation depicting the above information.[1]
IIWrite the corresponding quadratic equation in standard form.[1]
IIIWhat should be the new dimensions of the enlarged photo? OR Can any rational value of $x$ make the new area equal to $220$ cm $^{2}$ ?[2]

Answer

(I)

(18 + x) (12 + x) = 432

; (II)

x^{2} + 30 x - 216 = 0

; (III)

x = 6

, so the new photo is

24

cm by

18

cm. OR: for area

220

, the discriminant

916

is not a perfect square, so no rational value of

x

works.

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