Question

A palm tree casts a shadow that is 7 m shorter than its height. The distance from the top of the tree to the tip of the shadow is 1 m longer than the tree itself. How tall is the palm tree?

Answer 1

12 m

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:

`(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)`

• 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.