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Answer:
The palm tree is 12 m tall.
Step-by-step explanation:
1. The first to see is to consider this as triangle formed by the palm tree, the shadow, and the line from the top of the tree to the tip of the shadow to the tip the palm.
2. Assign variables to each distance in the triangle
Palm length= X
Shadow length= y
line from the top of the tree to the tip of the shadow to the tip the palm = Z
3. Describe the equation, reading the text:
(1) y=x-7
(2) z=x+1
(3) (this last one is from pitagoras theorem)
4. We solve the system:
{y = x - 7, z = x + 1, z^2 = x^2 + y^2}
Solutions
x = 4, y = -3, z = 5
x = 12, y = 5, z = 13
Since the distance can't be negative. The answer is the palm tree is 12 meters tall.
https://www.wolframalpha.com/input/?i=y%3Dx-7%3B+z%3Dx%2B1%3Bz%5E2%3Dx%5E2%2By%5E2