Answer
The value of x is 6.2 units .
Step-by-step explanation:
Now by using the pythagorean theorem
Hypotenuse² = Perpendicular² + Base²
Now in the Δ ABD
As given
DB² = DA² + AB²
As given
DB = 13 units
AB = 9 units
Putting values in the above
13² = 9²+ DA²
169 - 81 = DA²
88 = DA²
[tex]DA = \sqrt{88}[/tex]
In ΔABC
AB² = AC² + CB²
(As given AB = 9 units , CB = x)
9² = AC² + x²
AC ² = 81 - x²
Now in ΔADC.
AD² = AC² + DC ²
As
AC ² = 81 - x²
DC = 13 - x
[tex]AD = \sqrt{88}[/tex]
[tex](\sqrt{88})^{2}=81-x^{2} + (13-x)^{2}[/tex]
(By using the formula (a + b)² = a² + b² + 2ab )
[tex]88=81-x^{2} + 13^{2}-2\times 13\times x + x^{2}[/tex]
[tex]88=81-x^{2} + 13^{2}-26x+ x^{2}[/tex]
88-81 - 169 = -26x
88-250 =-26x
-162 = - 26x
[tex]x = \frac{162}{26}[/tex]
x = 6.2 (Approx)
Therefore the value of x is 6.2 units .
