In a triangle $A B C$ , perpendicular $A D$ from $A$ on $B C$ meets at $D .$ If $B D = 8 c m$ , $D C = 2 c m$ and $A D = 4 c m,$ then ___.

$Δ A B C$ is isosceles

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$Δ A B C$ is equilateral

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$A C = 2 A B$

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$Δ A B C$ is right angled at $A$

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Solution

The correct option is C
$A C = 2 A B$

In $Δ A D C,$

$A C^{2} = A D^{2} + D C^{2}$

$\Rightarrow A C^{2} = 4^{2} + 4 = 20$

$\Rightarrow A C = \sqrt{20} c m$ ... (i)

In $△ A D B,$

$A B^{2} = 4^{2} + 8^{2} = 80$

$\Rightarrow A B = \sqrt{80} = 2 \sqrt{20} c m$ ... (ii)

From (i) and (ii,) we get $A C = 2 A B$

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Similar questions

Q. In a ∆ABC, perpendicular AD from A and BC meets BC at D. If BD = 8 cm, DC = 2 cm and AD = 4 cm, then

(a) ∆ABC is isosceles
(b) ∆ABC is equilateral
(c) AC = 2AB
(d) ∆ABC is right-angled at A

In a $△ A B C$ , perpendicular $A D$ from $A$ on $B C$ meets at $D$ . If $B D = 8 cm, D C = 2 cm$ and $A D = 4 cm$ , then:

In $Δ$ ABC, a perpendicular AD is brawn to BC. If BD= 8 cm, DC = 2 cm and AD= 4 cm, then ___.

Δ A B C

is a right-angled triangle right angled at

B .

B D

is perpendicular to

A C .

A D = 8 c m

and

D C = 2 c m,

then find the length of

B D .

In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then angle BAC is ________

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In a triangle ABC, perpendicular AD from A on BC meets at D. If BD=8 cm, DC=2 cm and AD=4 cm, then ___.

The correct option is C AC=2AB In ΔADC, AC2=AD2+DC2 ⇒AC2=42+4=20 ⇒AC=√20cm ... (i) In △ADB, AB2=42+82=80 ⇒AB=√80=2√20 cm ... (ii) From (i) and (ii,) we get AC=2AB

In a triangle $A B C$ , perpendicular $A D$ from $A$ on $B C$ meets at $D .$ If $B D = 8 c m$ , $D C = 2 c m$ and $A D = 4 c m,$ then ___.