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# In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK

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In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK  [#permalink]

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Updated on: 16 May 2016, 07:02
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Difficulty:

15% (low)

Question Stats:

87% (01:32) correct 13% (01:24) wrong based on 37 sessions

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In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK = 20, what is the area of the triangle HEK?

A. 50
B. 75
C. 25√2
D. 100
E. 50√2

ALL THE BEST!

Originally posted by HARRY113 on 16 May 2016, 04:57.
Last edited by HARRY113 on 16 May 2016, 07:02, edited 2 times in total.
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In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK  [#permalink]

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16 May 2016, 05:10
1
HARRY113 wrote:
In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK = 20, what is the area of the triangle HEK?

A. 50
B. 75
C. 25√2
D. 100
E. 50√2

ALL THE BEST!

Hit Kudos if you like this post!

Hi,
This is in noway anywhere close to 700 level..
1) HYP = $$10\sqrt{2}$$..
Other two sides = 20 or 10+10..
Area = 1/2 *10*10 = 50
2) Sum of square of side = hyp^2..
$$(EH+HK)^2 = EH^2+HK^2+2*EH*HK = EK^2+2*EH*HK =20^2$$...
$$(10\sqrt{2})^2 +2*EH*HK =400............................ 2*EH*HK =400-200=200....$$
or $$EH*HK = 100..$$
area = $$\frac{1}{2}*EH*HK = \frac{1}{2}*100 = 50$$

A
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Re: In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK  [#permalink]

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16 May 2016, 11:09
HARRY113 wrote:
In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK = 20, what is the area of the triangle HEK?

A. 50
B. 75
C. 25√2
D. 100
E. 50√2

ALL THE BEST!

Attachment:

Triangle.png [ 3.68 KiB | Viewed 857 times ]

$$(10√2)^2$$ = $$x^2 + y^2$$

$$200$$ = $$(x + y)^2$$$$- 2xy$$

$$200$$ = $$(20)^2$$$$- 2xy$$

$$200$$ = $$400$$$$- 2xy$$

$$- 200$$ = $$- 2xy$$

$$xy = 100$$

Area of the triangle will be 1/2*xy = 50

Answer will be (A) 50 ; same opinion as chetan2u , not a 700 level question
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Re: In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK  [#permalink]

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18 Mar 2018, 13:18
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Re: In right triangle HEK, HK is the hypotenuse. If HK is 10√2 and EH + EK   [#permalink] 18 Mar 2018, 13:18
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