A picture frame has a ratio of length to width of 6 to 4.If the width is 36 centimeters, how many centimeters is the length of the picture frame?

54

Step-by-step explanation:

The ratio of 6 to 4 between the length and the with means that if the length was 6, the width would be 4.

We can represent this in a table:

Length         Width

     6       ⇒       4

and we need to find the length for a picture frame that has a width of 36. If we represent the length of the picture frame by x, and we update the previous table:

Length         Width

     6       ⇒       4

     x       ⇒       36

The value of x (the length) can be found by the rule of three: Multiply the cross quantities in the last table ( 6 by 36) and divide the result by the remaining value (4).

We get the following for x:

x = 6*36/4

x= 216 / 4

x = 54

The length is 54.

Another way to find the result is:

The width of the frame (36) is 9 times more than the width that the ratio indicates (4). Because

4*9 = 36

thus, the same must be true for the relationship between the length in the indicated ratio and the length of the frame (9 times bigger):

6*9 = 54

we also get 54 as the result.

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