Arectangular photograph is 8 cm wide and 12 cm long. the photograph is enlarged by increasing the length and width by an equal amount in order to double its area. what are the dimensions of the new photograph?

a.
12 cm by 16 cm
c.
20 cm by 30 cm
b.
16 cm by 24 cm
d.
48 cm by 72 cm

Answer with Step-by-step explanation:

A rectangular photograph is 8 cm wide and 12 cm long.

Area of rectangle=12×8

The photograph is enlarged by increasing the length and width by an equal amount.

Let its length and width be increased by x units.

i.e. New length=12+x

and New width=8+x

New Area=New length×New width

                =(12+x)(8+x)

On enlarging the area id doubled

i.e. New Area=2×(12×8)

       ⇒  (12+x)(8+x)=2×(12×8)

       ⇒ 12(8+x)+x(8+x)=2×96

       ⇒ 96+12x+8x+x²=192

       ⇒ x²+20x-96=0

       ⇒ x²+24x-4x-96=0

       ⇒ x(x+24)-4(x+24)=0

       ⇒ (x-4)(x+24)=0

       ⇒ either x-4=0 or x+24=0

i.e. either x=4 or x= -24

x can't be negative so x=4

New length=12+4=16 cm

New width=8+4=12 cm

Hence, Dimensions of new photograph are:

a.

12 cm by 16 cm

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