Question

If equilateral triangle ABC ad perpendicular BC prove that 3 BC square is equal to 4ADsquare

Answer 1

hence proved see the photo

Answer 2

Hence Proved.

Step-by-step explanation:

Given,

Equilateral $\triangle ABC$ where $AD\perp BC$ then proved that $3BC^{2} =4AD^{2}$

Let,

All sides $AB=BC=AC=x$ and $AD=h$

From $\triangle ABD$ as shown in figure,

 $AB^{2} =AD^{2} +BD^{2}$

⇒$x^{2} =h^{2} +(\frac{x}{2}) ^{2}$

⇒$h^{2} =x^{2} -(\frac{x}{2} )^{2}$

⇒$h^{2} =\frac{4x^{2}-x^{2} }{4}$

⇒$3x^{2} =4h^{2}$

Plug $x$ and $h$ values,

∴ $3BC^{2} =4AD^{2}$

Hence Proved.