Answer:
AD = 60
Explanation:
→If DE ║ AB is given , then ∠E ≅∠B and ∠D ≅ ∠A ( corresponding angles are congruent) there for ΔCDE ≈ ΔCAB ( because of the AA similarity theorem.)
→Since ΔCDE ≈ ΔCAB then their sides are in proportion so we write the proportions:
CD / CA = CE / CB
→substitute the sides with what is given in the picture, and find x so we can further find AD.
5x / 5x+2x-4 = 8x / 8x+3x, combine like terms
5x / 7x-4 = 8x / 11x, cross multiply
5x * 11x = 8x *(7x-4), multiply and distribute multiplication over subtraction
55x² = 56x² - 32x, subtract 56x² and add 32x to both sides of the equation
55x² - 56x² +32x = 0, combine like terms
-x² +32x = 0, factor -x
-x(x-32) = 0, so there are 2 possibly situation
→ Find x then substitute in AD = 2x-4 to find AD
-x = 0 so x = 0, will give us AD = 2x-4 = 2*0 -4 = -4, we reject this solution because a length can not be negative
x-32 = 0 so x= 32, will give us AD = 2x -4 = 2*32 -4 = 64 -4 = 60.