Question

Reading and similar triangles

In the diagram below of MADE, B is a point on AE and C
is a point on AD such that BC is parallel to ED. AC = x - 5,
AB = 15, BE = 40,, and AD = 2x + 3. Find the value of x
and the length of CD
A

Answer 1

• x = 12.8
• CD = 20.8

Explanation:

The parallel lines create similar triangles, so corresponding sides are proportional.

AC/AD = AB/AE

(x -5)/(2x +3) = 15/(15+40)

Cross-multiplying gives ...

55(x -5) = 15(2x +3)

55x -275 = 30x +45 . . . . eliminate parentheses

25x = 320 . . . . . . . . . . . . add 275-30x

x = 12.8 . . . . . . . . . . . . . . .divide by 25

__

CD = AD -AC = (2x +3) -(x -5) = x +8 = 12.8 +8

CD = 20.8