Question

From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.

Select one:

a.
36


b.
9


c.
16


d.
6

Answer 1

Answer: 6

Explanation:

By the geometric mean theorem,

`(BD)/(3)=(27)/(BD)\\\\(BD)^(2)=81\\\\BD=9\\\\\implies x=9-3=6`

Answer 2

x = 6

Explanation:

BD is the height of the triangle.

We can find the height of this triangle using one of the Euclidian Theorem:

h^2 = AD*DC rewrite the equation using the given information

(x + 3)^2 = 3*27 multiply

(x + 3)^2 = 81 find the root of both sides

x + 3 = 9 subtract 3 from both sides

x = 6