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# If the hypotenuse of the triangle in the figure has a length of 9, wha

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Math Expert
Joined: 02 Sep 2009
Posts: 58316
If the hypotenuse of the triangle in the figure has a length of 9, wha  [#permalink]

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13 Feb 2019, 01:03
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Difficulty:

35% (medium)

Question Stats:

64% (01:23) correct 36% (01:18) wrong based on 45 sessions

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If the hypotenuse of the triangle in the figure has a length of 9, what is x?

(A) 4.5

(B) 6

(C) $$\sqrt{40.5}$$

(D) $$\sqrt{45}$$

(E) $$\sqrt{162}$$

Attachment:

2019-02-13_1201.png [ 5.62 KiB | Viewed 562 times ]

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If the hypotenuse of the triangle in the figure has a length of 9, wha  [#permalink]

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Updated on: 13 Feb 2019, 05:55
Bunuel wrote:
If the hypotenuse of the triangle in the figure has a length of 9, what is x?

(A) 4.5

(B) 6

(C) $$\sqrt{40.5}$$

(D) $$\sqrt{45}$$

(E) $$\sqrt{162}$$

45:45:90
x:x:x√2

x√2=9
x= 9/√2 = ~6 IMO C
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Originally posted by Archit3110 on 13 Feb 2019, 05:28.
Last edited by Archit3110 on 13 Feb 2019, 05:55, edited 2 times in total.
Math Expert
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Posts: 58316
Re: If the hypotenuse of the triangle in the figure has a length of 9, wha  [#permalink]

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13 Feb 2019, 05:40
Archit3110 wrote:
Bunuel wrote:
If the hypotenuse of the triangle in the figure has a length of 9, what is x?

(A) 4.5

(B) 6

(C) $$\sqrt{40.5}$$

(D) $$\sqrt{45}$$

(E) $$\sqrt{162}$$

Bunuel
figure is missing.

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Fixed that. Thank you.
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Re: If the hypotenuse of the triangle in the figure has a length of 9, wha  [#permalink]

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13 Feb 2019, 05:50
Bunuel wrote:

If the hypotenuse of the triangle in the figure has a length of 9, what is x?

(A) 4.5

(B) 6

(C) $$\sqrt{40.5}$$

(D) $$\sqrt{45}$$

(E) $$\sqrt{162}$$

Attachment:
2019-02-13_1201.png

IMO C

$$x^2 + x^2 = 81$$
2$$x^2$$ = 81

x = 9/ root2

x = 4.5 * root2

x ~ 6.4
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Re: If the hypotenuse of the triangle in the figure has a length of 9, wha  [#permalink]

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13 Feb 2019, 06:30
Bunuel wrote:

If the hypotenuse of the triangle in the figure has a length of 9, what is x?

(A) 4.5

(B) 6

(C) $$\sqrt{40.5}$$

(D) $$\sqrt{45}$$

(E) $$\sqrt{162}$$

Attachment:
2019-02-13_1201.png

As it is isosceles right angle triangle x=hypotenuse/sqrt(2)

Hence $$x=9/\sqrt{2}$$ ==> 6.3

Hence C
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Re: If the hypotenuse of the triangle in the figure has a length of 9, wha  [#permalink]

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15 Feb 2019, 18:26
Bunuel wrote:

If the hypotenuse of the triangle in the figure has a length of 9, what is x?

(A) 4.5

(B) 6

(C) $$\sqrt{40.5}$$

(D) $$\sqrt{45}$$

(E) $$\sqrt{162}$$

Attachment:
2019-02-13_1201.png

Using the Pythagorean theorem, we can create the equation:

x^2 + x^2 = 9^2

2x^2 = 81

x^2 = 40.5

x = √40.5

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Re: If the hypotenuse of the triangle in the figure has a length of 9, wha   [#permalink] 15 Feb 2019, 18:26
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