Question

At a certain time of day, a tree that is x meters tall casts a shadow that is x−14 meters long. If the distance from the top of the tree to the end of the shadow is x+4 meters, what is the height, x, of the tree?
At a certain time of day, a tree that is x meters tall casts a shadow that is x−14 meters long. If the distance from the top of the tree to the end of the shadow is x+4 meters, what is the height, x, of the tree?

Answer 1

Answer: 30 meters

Step-by-step explanation:

This is the application of Pythagoras theorem,

the hypotenuse here is (x+4)

Applying the theorem , we have

$(x+4)^{2}$ = $x^{2}$ + $(x-14)^{2}$

expanding , we have

$x^{2}$ + 8x + 16 = $x^{2}$ + $x^{2}$  - 28x + 196

$x^{2}$ + 8x + 16 = 2$x^{2}$ - 28x + 196

re arranging the equation , we have

2$x^{2}$ - $x^{2}$  - 28x - 8x + 196 - 16 = 0

$x^{2}$ - 36x  + 180 = 0

factorizing the quadratic equation , we have

(x-30)(x-6) = 0

Therefore , x = 30 or x = 6

With the statement , since x -14 is the shadow , which can not be negative , so x = 30