Question

In the given figure, if AD perpendicular BC and
BD = 2, AC = 4, then value of AB2+CD2 is​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

AB2+CD2=20

Step-by-step explanation:

Given:

Here, BD = 2, AC = 4

Also AD ⊥ BC .

To find:

$AB^2+CD^2=?$

Solution:

Now as it is given that AD ⊥ BC, so ∠ ADB =90°

In Δ ADC,

Using Pythagoras theorem, we get

$AC^2= AD^2+CD^2$                 [1]

Also, ∠ ADC =90°                    [given]

In Δ ADB,

Using Pythagoras theorem, we get

$AB^2= AD^2+BD^2$                  [2]

Now subtract Eq 1 from 2, we get

$AB^2 -AC^2=( AD^2+BD^2)- (AD^2+CD^2)$

$AB^2 -AC^2=AD^2+BD^2- AD^2-CD^2$

$AB^2 -AC^2=BD^2-CD^2$

$AB^2+CD^2 =BD^2+AC^2$

$AB^2+CD^2 =(2)^2+(4)^2$

$AB^2+CD^2 =4+16$

$AB^2+CD^2 =20$