Question

Madeline is standing 2x−4 feet from the base of a tree. The height of the tree is 5x+6 feet. Find the equation that shows the straight-line distance from Madeline's feet to the top of the tree in terms of x. Do not simplify your answer (leave the answer in factored form).

Answer 1

Required equation is
`√((2x-4)^2+(5x+6)^2)`.

Explanation:

Given,

Height of the tree=5x+6

Distance from feet of the tree=2x-4

To find straight distance from feet of Madeline to top of the tree.

Let the tree as y-axis and distance from base along x-axis. Then the distence of straight line from foot of Madeline to top is become the hypotenuse of the triangle. Thus if we let,

Distance from feet of Madeline to top of tree= p, then, according to law of finding third side of a triangle we get,

`p^2=(\textit{distance from base})^2+(\textit{height of tree})^2`

`\therefore p=√((2x-4)^2+(5x+6)^2)`

Hence the result.