Answer:
12 m
Step-by-step explanation:
Take a look at the picture below.
If we call x the height of the tree, then the shadow which is 7 m shorter than its height would be "x - 7" and the distance from the top of the tree to the tip of the shadow would be "x + 1" (it is 1 m longer than the tree)
- We can see that we have a triangle rectangle so we can use the Pythagorean theorem:
[tex](x+1)^{2} = x^{2} + (x-7)^{2} \\x^{2} +2x+1=x^{2} +x^{2} -14x+49\\x^{2} +2x+1=2x^{2} -14x+49\\0=x^{2} -16x+48\\0=(x-12)(x-4)[/tex]
- From this we get that x = 12 and x = 4
- However, if the height of the tree was 4, the shadow would be 4 - 7 = -3 which cannot be possible. Therefore, x = 4 is not a solution for this problem
Thus, the only solution we have is x = 12 and the height of the palm tree is 12 m.
