Question

What is the value of x?

Answer 1

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

$DA = \sqrt{88}$

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

$AD = \sqrt{88}$

$(\sqrt{88})^{2}=81-x^{2} + (13-x)^{2}$

(By using the formula (a + b)² = a² + b² + 2ab )

$88=81-x^{2} + 13^{2}-2\times 13\times x + x^{2}$

$88=81-x^{2} + 13^{2}-26x+ x^{2}$

88-81 - 169 = -26x

88-250 =-26x

-162 = - 26x

$x = \frac{162}{26}$

x = 6.2 (Approx)

Therefore the value of x is 6.2 units .