A photograph measure 2 1/4 centimeters high and 5 centimeters wide. How high will the photograph be if it is enlarged to 12 centimeters wide?

Question

explained above

Answer 1

We can set up a proportion.

2 1/4 is to 5  as  x is to 12 ... or

 

(2 1/4)/5 = x/12

solve for x which will be the new height.

(9/4)/5 = x/12

9/20 = x/12

 

 

 

multiply both sides by 12

 

12(9/20)= x

x = 5 2/5 or 5.4 cm

 

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Another way to do this problem is simply to see by what factor the

width changed and apply that same factor to the height.

 

5x = 12

x = 12/5

 

The width was multiplied by 12/5 so

the new height is the old height times 12/5

 

Height = (2 1/4)(12/5)

          = (9/4)(12/5)

          = 27/5

          = 5 2/5 cm

 

 

 

 

Answer 2

We assume that the aspect ratio remains the same.  The aspect ratio is the ratio of width to height.

 

R = W/H

R = 5/2.25

R = 2.22

 

To calculate the new height, H, we isolate H on the left:

RH = W       multiply both sides by H

H = W/R      divide both sides by R

 

We know R, the ratio from above:

 

H = W/2.22

 

We substitute the new width for W

 

H = 12/2.22

 

H = 5.4