Question

In the figure , ∠ = 90 , ⊥ . ℎ 2 2 =

explain/prove the answer ​

Answer 1

Answer:

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In the given figure, ∠B<90 and segment AD ⊥ BC, show that

(i) b

2

=h

2

+a

2

+x

2

−2ax

(ii) b

2

=a

2

+c

2

−2ax

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Easy

Solution

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As △ADC is right angled at D

So applying Pythagoras theorem states that AC

2

=AD

2

+DC

2

b

2

=h

2

+(a−x)

2

b

2

=h

2

+a

2

+x

2

−2ax (1)

Hence (i) proved.

Also, △ADB is right-angled at D.

So applying Pythagoras theorem states that c

2

=h

2

+x

2

(2)

Substituting (2) in (1)

b

2

=h

2

+x

2

+a

2

−2ax

b

2

=(h

2

+x

2

)+a

2

−2ax

b

2

=c

2

+a

2

−2ax

b

2

=a

2

+c

2

−2ax

Hence (ii) proved.