Step-by-step explanation:
△ABE is similar to △DCE.
So,
AB / CD = AE / DE
12 / 10 = ( 2x + 4 ) / ( x + 8 )
6 / 5 = ( 2x / 4 ) / ( x + 8 )
Cross multiply,
5 * ( 2x + 4 ) = 6 * ( x + 8 )
10x + 20 = 6x + 48
10x - 6x = 48 - 20
4x = 28
x = 28 / 4
x = 7
AE = 2x + 4
Substitute x = 7 in 2x + 4,
2x + 4
= 2 ( 7 ) + 4
= 14 + 4
= 18
So,
AE = 18 units
