Question

At a certain time of day, a tree that is x meters tall casts a shadow that is x-28 meters long. If the distance from the top of the tree to the end of the shadow is x + 8 meters what is the height x of the tree?

Answer 1

Tree height = 45ft

Tree's shadow = 28ft

Distance from top of

tree to tip of shadow.

= 53ft.

Explanation:

Tree = x

Shadow = x - 17

Distance from top of tree

to end of shadow = x + 8

So x^2 + (x - 17)^2 = (x + 8)^2

x^2 +(x^2 - 34x + 289) = (x^2 + 16x + 64)

Combine and collect like terms.

x^2 - 50x + 225

(x - 5)(x - 45)

So either x = 5 or x = 45

As the shadow = (x - 17) I would

discount x = 5.