Answer:
Therefore the tree is 15 feet tall.
Step-by-step explanation:
Given, you are 5 feet tall standing 3 feet away from a mirror.
Here height is directly proportional to the distance from mirror.
Directly proportional: When both objects increase simultaneously. Then the relation between objects is directly proportional.
∴height ∝distance from mirror
⇒height = k× distance from mirror
Here k is proportional constant.
[tex]\Rightarrow \frac{Height}{distance from mirror} =k[/tex]
[tex]\Rightarrow \frac{5}{3} =k[/tex] [ since height = 5 feet and distance from mirror=3]
Again given, The top of the tree and the base of the tree is 9 feet away from the mirror.
Let the tree be h feet tall.
[tex]\therefore\frac{h}{9}=k[/tex] [ Here height = h and distance from mirror=9]
[tex]\Rightarrow \frac{h}{9} =\frac{5}{3}[/tex] [tex][\because \frac{5}{3} =k][/tex]
[tex]\Rightarrow h =\frac{5\times 9}{3}[/tex]
Therefore h=15
Therefore the tree is 15 feet tall.
