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# In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =

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Joined: 02 Sep 2009
Posts: 53066
In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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09 Oct 2018, 00:36
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Difficulty:

15% (low)

Question Stats:

88% (01:17) correct 12% (01:11) wrong based on 49 sessions

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In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =

(A) 12
(B) 13
(C) 15
(D) 17
(E) 24

Attachment:

triangle.jpg [ 14.4 KiB | Viewed 578 times ]

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Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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09 Oct 2018, 00:48
Bunuel wrote:

In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =

(A) 12
(B) 13
(C) 15
(D) 17
(E) 24

Attachment:
triangle.jpg

From the measure of various sites of triangle ABC, we can see that it is a right angle triangle whose right angle is at Angle B.

Applying Pythagoras theorem to triangle ABD: we can find the measure of AD.

AD=17, hence option D is the correct one.
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Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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09 Oct 2018, 06:11
How can we assume that the triangle is right angled triangle. Neither the angle is given in the figure nor it is said "Drawn to Scale"
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Joined: 02 Sep 2009
Posts: 53066
Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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09 Oct 2018, 06:30
shashaankbhat wrote:
How can we assume that the triangle is right angled triangle. Neither the angle is given in the figure nor it is said "Drawn to Scale"

AB = 8, BC = 6, AC = 10 satisfy AB^2 + BC^2 = AC^2, so the triangle is indeed right-angled at B.
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Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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09 Oct 2018, 06:33
Ah missed it. Thank you very much for the explanation Bunuel
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Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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09 Oct 2018, 06:41
Bunuel wrote:

In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =

(A) 12
(B) 13
(C) 15
(D) 17
(E) 24

Attachment:
triangle.jpg

$$AB = 8$$ & $$BD = 15$$ in the right Angled Triangle..

SO, Hypotenuse $$AD = 17$$ , following Pythagorean triple (8, 15, 17) , Answer must be (D)

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Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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09 Oct 2018, 08:29
Bunuel wrote:

In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =

(A) 12
(B) 13
(C) 15
(D) 17
(E) 24

Attachment:
triangle.jpg

$$AB = 8, BC = 6, AC = 10$$ tell us that it is a right angle triangle. $$AC = \sqrt{15^2 + 8^2} = 17$$

Another way (probably easier).

Any side of the triangle cannot be more than that of the sum of the other two sides.
Sum of the other two sides = 23

Hypotenuse is the largest side of a right angle triangle. We already have a base of 15.

Only one option remains.

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Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =  [#permalink]

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12 Oct 2018, 06:54
Bunuel wrote:

In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =

(A) 12
(B) 13
(C) 15
(D) 17
(E) 24

Attachment:
triangle.jpg

Since triangle ABC is a 6-8-10 triangle, it’s a right triangle with right angle at B. We can find AD, the hypotenuse of right triangle ABD, using the Pythagorean theorem,

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Re: In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD =   [#permalink] 12 Oct 2018, 06:54
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