Question

6. Observe the figure and find the length of side AD in cm. (2) 16 (1) 8/2 (3) 8 (4) 32​

Answer 1

In ∆ABC, Angle B is 90°

By Pythagoras theorem,

AC²=AB²+BC²

AC²=4²+4²

AC²=16+16

AC²=32

AC=√32

AC=√16x2

AC=4√2cm

Now, In ∆ACD, Angle C is 90°

By Pythagoras theorem,

AD²=AC²+CD²

AD²=(4√2)²+(4√2)²

AD²=16x2+16x2

AD²=32+32

AD²=64

AD=√64

AD=8cm

Therefore, The value of AD=8cm

Answer 2

Answer: option is correct

Step-by-step explanation:

In ∆ABC

(AC)*=AB*+BC*

(AC)*=4*+4*

(AC)*=16+16

AC=√32

AC=√16×2=4√2

So,AC=CD=4√2

In∆ADC

(AD)*=AC*+CD*

AD*=(4√2)+(4√2)

AD*=16×2+16×2

AD*=32+32

AD=√64

AD=8cm