A tree casts a shadow of 27 feet. A person 5 feet tall casts a shadow of 2 feet. What is the height of the tree?
2007-08-08 17:08:01 · 13 answers · asked by michelah b 2 in Science & Mathematics ➔ Mathematics
Make two fractions, one representing the tree and its shadow, the other representing the person and his/her shadow. Set equal as they are proportional. Solve by cross-multiplying.
tree height over shadow = person height over shadow
x/27 = 5/2
2x = 135 ft
x = 67.5 ft
2007-08-08 17:13:06 · answer #1 · answered by dwalon2 4 · 1⤊ 0⤋
If a person that is 5 feet tall casts a shadow only 2 feet long then divide five by two and you get 2.5. Then multiply 27 by 2.5 and you get your answer. Just write it out like this: 5:2 = ?:27. It might also help you to draw a picture. The answer is 67.5 feet. There are alot of different ways to work out this problem.
2007-08-08 17:16:09 · answer #2 · answered by Matt 2 · 0⤊ 1⤋
Set a proportion.
height of tree is to 5 as 27 is to 2.
x / 27 = 5 / 2
cross multiply
2x = 135
divide by 2
x = 67.5
2007-08-08 17:11:52 · answer #3 · answered by this_1ove_x3 2 · 1⤊ 0⤋
There is a ratio of height of the object to its shadow length. So the person's ratio is 5 ft/ 2 ft. The tree's ratio is x ft/ 27 ft. Make these ratios equal and you can solve for the missing part...
5/2 = x/27
2x = 135
x = 135/2
x = 67.5 ft
So the tree is 67.5 ft tall.
2007-08-08 17:12:01 · answer #4 · answered by JO 3 · 1⤊ 0⤋
Let the height of the tree be x m.
Using similar triangles,
x/27 = 5/2
2x = 5(27)
x = 67.5
Therefore, the height of the tree is 67.5 m.
2007-08-08 17:11:56 · answer #5 · answered by Anonymous · 1⤊ 0⤋
number of times 2 goes into 27 13.5 and then multiply by 5=67.5 easy way
lol
2007-08-08 17:18:31 · answer #6 · answered by fattybumbalatty 2 · 1⤊ 0⤋
x / 27 = 5 / 2
cross multiply
2x = 135
divide by 2
x = 67.5
2007-08-08 17:15:57 · answer #7 · answered by Anonymous · 1⤊ 0⤋
27 feet / (2 feet / 5 feet) = 67,5 feet = 7 * 10^1 feet [rounded to 1 digit]
2007-08-08 17:16:37 · answer #8 · answered by Anonymous · 0⤊ 1⤋
ground, shadows, and verticals make similar triangles whose sides are in proportion. t is height of tree.
t/27 = 5/2
2t = 135
t = 67.5 ft.
2007-08-08 17:12:49 · answer #9 · answered by Philo 7 · 1⤊ 0⤋
its a direct relationship shadow/height of tree = shadow/height of person
27/x=5/2
x=10.8ft
2007-08-08 17:12:16 · answer #10 · answered by lolli_pop_princez889 2 · 0⤊ 1⤋