In the following figure AE perpendicular to BC, D is the midpoint of BC, then x is equal to

To find the value of x, we can use the properties of perpendicular lines and midpoints.

1. Since AE is perpendicular to BC, we know that the angle AED is a right angle.

2. Since D is the midpoint of BC, we can conclude that BD is equal to DC.

3. Let's denote the length of BD as y. Therefore, DC is also equal to y.

4. Using the Pythagorean theorem in triangle AED, we can write the equation AE^2 = AD^2 + DE^2.

5. Since AD is equal to y (as BD = DC), we can rewrite the equation as AE^2 = y^2 + DE^2.

6. Now, let's consider triangle DEC. Since DE is the height of the right-angled triangle DEC, we can use the Pythagorean theorem again to write the equation DE^2 = DC^2 - EC^2.

7. Since DC is equal to y and EC is equal to x, we can rewrite the equation as DE^2 = y^2 - x^2.

8. Substituting this value of DE^2 into the equation from step 5, we get AE^2 = y^2 + (y^2 - x^2).

9. Simplifying the equation, we have AE^2 = 2y^2 - x^2.

10. Since AE is perpendicular to BC, we can conclude that AE is equal to BC.

11. Therefore, we can rewrite the equation as BC^2 = 2y^2 - x^2.

12. Since D is the midpoint of BC, we know that BC is equal to 2y.

13. Substituting this value into the equation from step 11, we get (2y)^2 = 2y^2 - x^2.

14. Simplifying the equation, we have 4y^2 = 2y^2 - x^2.

15. Rearranging the equation, we get x^2 = 2y^2 - 4y^2.

16. Simplifying further, we have x^2 = -2y^2.

17. Taking the square root of both sides, we get x = ±√(-2y^2).

18. Since we are dealing with lengths, we can ignore the negative square root.

19. Therefore, the value of x is x = √(-2y^2).

Please note that the value of x is dependent on the length of BD (or y), and without further information, we cannot determine the exact value of x.