Question

What is the value of x and the length of segment DE?

1.5=
2x
9
+ 3
2. 10x + 15 = 9(9)
2x + 3
x=
Length of DE =
units
Intro
Done

Answer 1

X= 6.6

DE= 16.2

Explanation:

Answer 2

x = 6.6; DE = 16.6

Explanation:

Assume the diagram is like the figure below.

1. Calculate the value of x

In a right triangle, the altitude drawn from the right angle to the hypotenuse divides the triangle into two similar triangles.

Thus, ∆CDF ~ ∆FDE, and

`\begin{array}{rcl}(CD)/(DF) &=& (FD)/(DE)\\\\(5)/(9) &=& (9)/(2x + 3)\\\\5(2x + 3) & = &81\\10x + 15 & = & 81\\10x & = & 66\\x & = & \mathbf{6.6}\\\end{array}`

2. Calculate the length of DE

DE = 2x + 3 = 2(6.6) + 3 = 13.2 + 3 = 16.2