A tree casts a shadow that measures 5 m. At the same time, a meter stick casts a shadow that is 0.4 m long. How tall is the tree?
Is this correct ?
1m=.4m
1m÷.4m =2.5m
2.5m X 5m =12.5m
they probably wanted you to set up 2 similar triangles and set up a ratio.
let the height of the tree be h m
then h/5 = 1/.4
cross-multiply to get .4h=5
h=5/.4 = 12.5 m
so the tree is 12.5 m high.
I know you got that numerical answer but I didn't like the way you made your statements
e.g.
1m = .4m makes no sense, 1m cannot be .4m
(I know this might seem petty, but to mathematicians this is just as grating as bad grammar is to an English teacher.)
To find the height of the tree, you can use similar triangles. The length of the tree's shadow is proportional to the height of the tree, just like the length of the meter stick's shadow is proportional to its height.
Using the given measurements:
Length of the tree's shadow = 5m
Length of the meter stick's shadow = 0.4m
We can set up the proportion:
Height of the tree/Length of the tree's shadow = Height of the meter stick/Length of the meter stick's shadow
Let's plug in the values:
Height of the tree/5m = Height of the meter stick/0.4m
Next, let's solve for the height of the tree:
Height of the tree = (Height of the meter stick/0.4m) * 5m
So, the height of the tree is (Height of the meter stick * 5) / 0.4.
You mentioned 1m = 0.4m, which is incorrect.
Actually, 1m is equal to 2.5m in this scenario.
So, the height of the tree is (Height of the meter stick * 5) / 0.4 = (1m * 5) / 0.4 = 12.5m.
Therefore, the correct height of the tree is 12.5m, not 5m as you mentioned.