Question : In the given figure, AB = 8 cm; AC = 17 cm. What is the length of AD?
Option 1: 4.68 cm
Option 2: 5.36 cm
Option 3: 3.76 cm
Option 4: 8.5 cm
Correct Answer: 3.76 cm
Solution :
Given: A right-angled triangle ABC with AB = 8 cm and AC = 17 cm
Applying the Pythagoras theorem to the given $\triangle$ABC
⇒ We get, AC
2
= AB
2
+ BC
2
⇒ 17
2
= 8
2
+ BC
2
⇒ BC
2
= 225
⇒ BC = 15 cm
Now, the above triangle ABC can be divided into two right triangles $\triangle$BDA and $\triangle$BDC.
Let the length of AD = $x$, then DC = 17 – $x$
Applying Pythagoras theorem to the two triangles we get,
⇒ BD
2
= AB
2
– AD
2
and BD
2
= BC
2
– DC
2
So, AB
2
– AD
2
= BC
2
– DC
2
⇒ 82 – $x$
2
= 15
2
– (17 – $x$)
2
⇒ 64 – $x$
2
= 225 – (289 + $x$
2
– 34$x$)
⇒ 64 – 225 + 289 = 34$x$
⇒ 128 = 34$x$
$\therefore x$ = 3.76 cm
Hence, the correct answer is 3.76 cm.
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