Question

Solve for x using figure to the right. Pls answer this it is urgent

Answer 1

Answer:

Therefore the value of x = 10 units

Step-by-step explanation:

Let label the Triangles first,

Δ ABC a right triangle at ∠ A =90°

Δ ADB andΔ ADC a right triangle at ∠ D =90°

Such that

AD = x

BD = 50

CD = 2

∴ BC = BD + DC = 50 + 2 = 52

To Find:

x = ?

Solution:

In right triangle  By Pythagoras Theorem,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

In right triangle Δ ADB andΔ ADC  By Pythagoras Theorem we will have,

AB² =  BD² + AD²

AB² = 50² + x²            ..................equation ( 1 )

and

AC² = DC² + AD²

AC² = 2² + x²             ...................equation ( 2 )

Now in right triangle Δ ABC,

BC² = AB² + AC²

Equating equation  (1 ) and ( 2 ) and the given value we get

52² = 50² + x² + 2² + x²

∴ 2x² = 2704 - 2504

∴ 2x² =200

∴ $x^{2} =\frac{200}{2}\\\\\therefore x=\pm\sqrt{100} \\\\ \textrm{x cannot be negative}\\\therefore x= 10\ unit$

Therefore the value of x = 10 units