# A photograph has a width of 9.5 cm and an area of 104.5 cm^2. An enlarged image is to be made that has a width of 19 cm. What will be its area?

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A photograph has a width of 9.5 cm and the corresponding area is 104.5 cm^2. It has to be enlarged to make the width equal to 19 cm. The length of the original image is 104.5/9.5 = 11 cm.

Assuming the ratio of the sides is kept the same in the enlarged image, as the width is changed from 9.5 to 19 cm it has been doubled, doing the same with the length gives 11*2 = 22 cm

**The new area of the photograph is 22*19 = 418 cm^2.**

Given : width of the photograph = 9.5 cm, Area = 104.5 cm^2

length(height) of the photograph = Area/width = 104.5/9.5 = 11cm

Now when a photograph is enlarged it is enlarged lengthwisw and

widthwise in the same proportion.

Since width of the enlarged photograph is given= **19cm** which means

the ratio by which width is enlarged = **19/9.5 = 2** therefore the

length also to be enlarged in the same **ratio 2** .

The length of the enlarged photograph = **11*2 = 22cm**

Area of the enlarged photograph = **22*19= 418 cm^2**

**Area of the enlargment = 418 cm^2 <--Answer**

The photograph has a width of 9·5 cm

and area of 104·5 cm^2

That means the height of the photograph =

Area/Width = 104·5 cm^2 / 9·5 cm

=11 cm

Enlargement means scaling (multiplying) the length and breadth by a number (n). We need to find out "n" and we must keep in mind that the ratio "height/widhth" should remain the same then only it is enlargement and the photograph won't become distorted.

So the ration:

r = height/widht

= 11 / 9.5

= 1.16

Given the enlarged width = 19 cm

so the factor by which the width was multiplied =

Enlarged width/ original width

= 19 / 9.5

= 2

So n = 2

Hence the new height becomes

Original height * n

= 11 * 2 cm

= 22 cm

Check the ratio between heighth and width:

r = 22 / 19 = 1.16 same as before, right ? It has to be as I told earlier.

Hence enlarged area (new area) = Enlarged Height * Enlarged Width

=22 * 19 cm^2

= 418 cm^2

If area of enlargement means the extra area generated by the enlargement with respect to the original area, then

area of enlargement = New area - original area

= (418 - 104.5) cm^2

= 313.5 cm^2

So,

**Enlarged area = 418 cm^2**

**Area of enlargement = 313.5 cm^2**