x = 37.5 (or) ![\frac{75}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B75%7D%7B2%7D)
Solution:
Given ![\triangle A B C \sim \triangle D B E](https://tex.z-dn.net/?f=%5Ctriangle%20A%20B%20C%20%5Csim%20%5Ctriangle%20D%20B%20E)
AC = 50, DE = 30, EC = 25, BE = x, BC = 25 + x
To find the value of x:
Property of similar triangles:
If two triangles are similar then the corresponding angles are congruent and the corresponding sides are in proportion.
![$\frac{BE}{BC} =\frac{DE}{AC}](https://tex.z-dn.net/?f=%24%5Cfrac%7BBE%7D%7BBC%7D%20%3D%5Cfrac%7BDE%7D%7BAC%7D)
![$\frac{x}{25+x} =\frac{30}{50}](https://tex.z-dn.net/?f=%24%5Cfrac%7Bx%7D%7B25%2Bx%7D%20%3D%5Cfrac%7B30%7D%7B50%7D)
Do cross multiplication, we get
![50x=30(25+x)](https://tex.z-dn.net/?f=50x%3D30%2825%2Bx%29)
![50x=750+30x](https://tex.z-dn.net/?f=50x%3D750%2B30x)
Subtract 30x from both sides of the equation.
![20x=750](https://tex.z-dn.net/?f=20x%3D750)
Divide by 20 on both sides of the equation, we get
x = 37.5 (or) ![\frac{75}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B75%7D%7B2%7D)
Hence the value of x is 37.5 or
.