Lifespan of bulbs(days)---------Number of bulbs

100< x <=120------------------------15

120< x <=160------------------------105

160< x <=180------------------------130

180< x <=220------------------------230

220< x <=240------------------------20

Question:

When a histogram is drawn to represent this information, the rectangle representing the bulbs with lifespan in the interval 100< x <=120 has width 2 cm and height 3 cm. Find the width and the height of the rectangle representing the bulbs with lifespan in the interval 180< x <=220.

I found this question from a book. the answer given is as follow:

Width

100 < x <=120 (20 units) -> 2 cm

180 < x <=220 (40 units) -> 4 cm

Height

15 bulbs -> 3 cm implies 1 bulb -> 0.2 cm

Thus for 180< x <=220, 230 bulbs -> 46 cm

I understand how to get the width. But I have a question regarding the height.

area of bar for 100<x<=120 is 2*3=6 cm square

6 cm square ->15 units implies 1 cm square -> 2.5 units

So area of bar for 180<x<=220 is 230/2.5=92 cm square

Since the width is 4 cm for the interval 180<x<=220

So the height is 92/4=23 cm!! which is half of the answer above!! I thought when the width of the two intervals are different, then we can't just use the ratio to find the height, there is something to do with the area, right?

Which answer is correct??? Why???

Furthermore, from wikipedia I found out that for histogram, the area of each bar has to be equal to the frequency. But obviously this is not true for the question above, right?

I'm quite confused about the concept, like when do we have to make sure that the area of each bar represents the frequency.

Can anyone help me? Urgent!! Test is coming....