MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

Answer: 30 metersStep-by-step explanation:This is the application of Pythagoras theorem,the hypotenuse here is (x+4) Applying the theorem , we have[tex](x+4)^{2}[/tex] = [tex]x^{2}[/tex] + [tex](x-14)^{2}[/tex]expanding , we have[tex]x^{2}[/tex] + 8x + 16 = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] - 28x + 196[tex]x^{2}[/tex] + 8x + 16 = 2[tex]x^{2}[/tex] - 28x + 196re arranging the equation , we have2[tex]x^{2}[/tex] - [tex]x^{2}[/tex] - 28x - 8x + 196 - 16 = 0[tex]x^{2}[/tex] - 36x + 180 = 0factorizing the quadratic equation , we have (x-30)(x-6) = 0Therefore , x = 30 or x = 6With the statement , since x -14 is the shadow , which can not be negative , so x = 30