A sports hall is in the shape of a large box or cuboid. The area of the floor is 200m2, the area of one of the side walls is 150m2 and the area of an end wall is 48m2. What is the height, in metres, of the hall?
I was helping my young daughter with this, a question from an entry exam for a school. For 11 year olds I thought it is actually very challenging, I worked it out as follows, I wonder if there is a simpler approach to these problems?
My working out:
Areas:
- 48m2 = h x w
- 200m2 = w x l
- 150m2 = h x l
I solved for h in both 1 and 3 above then set them equal:
48/w = 150/l
I then solved for w in 2 (w = 200/l) and substituted in for w in preceding equation:
48l/200 = 150/l
from there I got:
l^2(48/200) = 150
From where I solved for l and got l = 25, h = 6 and w = 8, so the height of the hall is 6m.
But this all feels not very intuitive for an 11 year old (or younger as my daughter is). Any suggestions on a better way to view this problem?
The ratio of the length and the width of the floor must be the same as the ratio between the areas of the side and end walls, which is 48/150 = 8/25. This means the floor is 8x25 and the height is 48/8=6 (or 150/25=6).