Question

If I am 5 feet tall standing 3 feet away from a mirror looking at a tree that I can barely see the top of and the base of the tree is 9 feet away from the mirror how tall is the tree?

Answer 1

Therefore the tree is 15 feet tall.

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.

`\Rightarrow (Height)/(distance from mirror) =k`

`\Rightarrow (5)/(3) =k` [ 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.

`\therefore(h)/(9)=k` [ Here height = h and distance from mirror=9]

`\Rightarrow (h)/(9) =(5)/(3)`
`[\because (5)/(3) =k]`

`\Rightarrow h =(5* 9)/(3)`

Therefore h=15

Therefore the tree is 15 feet tall.