At a point on the ground 24 ft from the base of a tree, the distance to the top of the tree is 4 ft more than 3 times the height of the tree. Find the height of the tree.

Therefore,

The height of the tree is 7 ft.

Step-by-step explanation:

Consider a diagram shown below such that

Let,

AB = h = height of tree

'C' is a point on the ground 24 ft from the base 'B' of a tree

BC = 24 ft

The distance to the top of the tree is 4 ft more than 3 times the height of the tree

AC =  4 + 3h

To Find:

AB = h = ? ( height of tree)

Solution:

In Right Angle Triangle ABC by Pythagoras theorem we have

Substituting the values we get

Using (A+B)²=A²+2AB+B² we get

Dividing through out by 8 we get

Which is a quadratic equation, so on factorizing we get

h cannot be negative therefore ,

Therefore,

The height of the tree is 7 ft.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b