If in an equilateral triangle ABC - AD is perpendicular to BC- then AD 2-A- 3-2 D C2B- 2 D C2C- 3 C D2D- 4 D C2

The correct option is C In Δ ABC, AD ⊥ BC. then, AC^2 = AD^2+CD^2 [By Pythagorus Theorem] ⇒ AD^2 = AC^2 CD^2 ⇒ AD^2= BC^2 CD^2 [since, AC=BC] ⇒ AD^2 =(2C ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Pythagoras Theorem

If in an equi...

Question

If in an equilateral triangle $△ A B C, A D$ is perpendicular to $B C,$ then $A D^{2} =$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

In $Δ A B C, A D ⊥ B C .$

then, $A C^{2} = A D^{2} + C D^{2}$ [By Pythagorus Theorem]

$\Rightarrow A D^{2} = A C^{2} - C D^{2}$

$\Rightarrow A D^{2} = B C^{2} - C D^{2}$ [since, $A C = B C$ ]

$\Rightarrow A D^{2} = (2 C D)^{2} - C D^{2}$ [since, $B C = 2 C D$ ]

$\Rightarrow A D^{2} = 3 C D^{2}$

Suggest Corrections

Similar questions

If $△ A B C$ is an equilateral triangle such that $A D$ is perpendicular to $B C$ , then $A D^{2} =$

Q. If ∆ABC is an equilateral triangle such that AD ⊥ BC, then AD² =

(a)

\frac{3}{2} {DC}^{2}

(b) 2 DC²
(c) 3 CD²
(d) 4 DC²

Q. In an equilateral triangle ABC if AD ⊥ BC, then AD² =

(a) CD²
(b) 2CD²
(c) 3CD²
(d) 4CD²

Q. In an equilateral triangle ABC, AD is drawn perpendicular to BC meeting BC in A. If

(A D)^{2} =

(B D)^{2}

. Find

x

If $Δ A B C$ is an equilateral triangle such that $A D$ is perpendicular to $B C,$ then $A D^{2}$ = ___.

Join BYJU'S Learning Program

If in an equilateral triangle △ABC, AD is perpendicular to BC, then AD2=

The correct option is C In ΔABC, AD⊥BC. then, AC2=AD2+CD2 [By Pythagorus Theorem] ⇒AD2=AC2−CD2 ⇒AD2=BC2−CD2 [since, AC=BC] ⇒AD2=(2CD)2−CD2 [since, BC=2CD] ⇒AD2=3CD2

If in an equilateral triangle $△ A B C, A D$ is perpendicular to $B C,$ then $A D^{2} =$