Question

in triangle ABC,angle B=90 degree bd is perpendicular to ac if ab =8 cm and bd=4cm what is the length of cd​

Answer 1

$\sf\large{Correct\: Question}$

In triangle ABD,angle B=90° if AB =8 cm and BD=4cm what is the length of AD

$\sf\large{Given:}$

$\sf{in\triangle\:ABD\: \angle\:B=90\degree}$

• $\sf{BD\:is\: perpendicular}$
• $\sf{AB=8cm\:\:and\:BD=4cm}$

$\sf\large{Let:}$

• $\sf{AB\:is\:base}$
• $\sf{BD\:is\: perpendicular}$
• $\sf{AD\:is\: hypotenous}$

$\sf\large{To\: Find:}$

• $\sf{The\: length\:of\:AD}$

$\rm{According\:to\:the\: Pythagoras\: theorem}$

$\rm{\implies P^2+b^2=h^2}$

$\rm{\implies AD^2=BD^2+AB^2}$

$\rm{\implies AD^2=4^2+8^2}$

$\rm{\implies AD^2=16+64}$

$\rm{\implies AD^2=80}$

$\rm{\implies AD=\sqrt{16*5}}$

$\rm\green{\implies AD=4\sqrt{5}}$

Hence,

$\sf\purple{\implies The\: length\:of\:AD=4\sqrt{5}cm}$

$\sf\large{Verification:}$

$\rm{\implies (4\sqrt{5})^2=4^2+8^2}$

$\rm{\implies 16\sqrt{25}=16+64}$

$\rm{\implies 16*5=16+64}$

$\rm\purple{\implies 80=80}$

$\sf\large\orange{\implies Hence, Verified}$

Answer 2

Answer:

Given:

∠ABC=90∘

BD is perpendicular to AC,

BD=8 and AD=4, according to the diagram.

Step by step explanation:

Let ∠ACB=x,⇒∠CBD=90−x

⇒∠ABD=x,⇒∠BAD=90−x

⇒ΔABC, ΔADB and ΔBDC are similar

⇒BD/CD=AD/DB

⇒8/CD=4/8

⇒CD=(8×8)/4

⇒CD=16

Conclusion:

The length of side CD is 16 cm.