Grades 3-4 Video Solutions 2021-video 2021 3-4/15

Video Transcription

Problem number 15. On a tall building there are four fire escape ladders as shown. The heights of three ladders are at their tops. What is the height of the shortest ladder?  A-12, B-14, C-16, D-20, or E-22. We know the height of the whole building. The shortest ladder has a gap here and a gap here.  We should be able to find the length of both these gaps and subtract them from 48, which is the height of the building, to get the height of the shortest ladder.  Notice that the ladder marked with a 36 runs from the very bottom up to the top of the shorter ladder. So we can find the length of this open area by subtracting 36 from 48.  48-36, 8-6 is 2, 4-3 is 1, so we get 12 here. For the gap on the bottom, we can subtract 32, which is the height of this ladder, from 48. 48-32, 8-2 is 6, 4-3 is 1, so that's 16.  So we know that 16 plus the height of this ladder plus 12 make 48. 12 plus 16 is 8, so the height of this ladder will be 48-28, or 20.  So the answer is D. 20 is the height of the shortest ladder.

Video Summary

The problem involves determining the height of the shortest ladder out of four fire escape ladders on a building. Given the building height of 48 and information that one ladder (36) reaches from the bottom to the top of the shorter ladder, it's necessary to find the lengths of gaps above and below the shortest ladder. By subtracting known ladder heights from 48, the gaps are found to be 12 and 16, respectively. Adding these gaps with the shortest ladder should equal 48, resulting in the shortest ladder's height being 20. Thus, the answer is D: 20.

Keywords

fire escape ladders

building height

gap calculation

shortest ladder

ladder height