Question

pls solve this question by method for ur help ans is 16 cm​

Answer 1

$\huge\underline\mathfrak\pink{Answer-}$

CD = 16cm.

$\huge\underline\mathfrak\pink{Explanation-}$

Given :

• In rt ∆ABC, angle A = 90°
• BD is perpendicular to AC
• BD = 8cm
• AD = 4cm

To find :

• Length of CD.

Solution :

∆DBA ~ ∆DCB

Reason : If a perpendicular is drawn from the vertex having an angle of 90° of a right angled ∆ to the hypotenuse, then the ∆s on each side of perpendicular are similar to each other and to the complete ∆.

$\therefore$ $\dfrac{BD}{CD}$ = $\dfrac{AD}{BD}$

$\rightarrow$ BD² = CD × AD

putting the given values,

$\rightarrow$ (8)² = 4 × CD

$\rightarrow$ 64 = 4 × CD

$\rightarrow$ CD = $\dfrac{64}{4}$

$\rightarrow$ CD = 16 cm ( required answer )