Question

15. Find the length of segment DE of the triangle ABC.

A. 24 units
B. 32 units
C. 26 units
D. 52 units

Answer 1

Option C.
`26\ units`

Explanation:

we know that

Triangles ADE and ABC are similar by AA similarity postulate

AB=2AD

Apply proportion

`(AD)/(AB)=(8x-6)/(12x+4)\\ \\(AD)/(2AD)=(8x-6)/(12x+4)\\ \\(1)/(2)=(8x-6)/(12x+4)\\ \\12x+4=16x-12\\ \\16x-12x=4+12\\ \\4x=16\\ \\x=4\ units`

Find the length of segment DE

`DE=8x-6=8(4)-6=26\ units`