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# Triangle XYZ is an isosceles right triangle. If side XY is longer than

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Math Expert
Joined: 02 Sep 2009
Posts: 50544
Triangle XYZ is an isosceles right triangle. If side XY is longer than  [#permalink]

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28 Jan 2015, 06:42
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Difficulty:

55% (hard)

Question Stats:

65% (01:32) correct 35% (02:03) wrong based on 199 sessions

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Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 16, what is the measure of side XY?

A. 4
B. 4√2
C. 8
D. 8√2
E. Cannot be determined from the information provided

Kudos for a correct solution.

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Math Expert
Joined: 02 Aug 2009
Posts: 7022
Re: Triangle XYZ is an isosceles right triangle. If side XY is longer than  [#permalink]

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28 Jan 2015, 08:31
1
ans C ..8..
xy being larger means it is the hyp..
area =(1/2)*(yz)^2=16 or yz=4*\sqrt{2}..
therefore hyp=xy=8
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Re: Triangle XYZ is an isosceles right triangle. If side XY is longer than  [#permalink]

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28 Jan 2015, 09:36
1/2 a^2 = 16
Side of triangle is 4 root 2
The ratio of sides of an isoceles triangle is 1:1:root 2.
There fore sides are in ratio of 4 root 2: 4 root 2: 8.
larger side is 8
Math Expert
Joined: 02 Sep 2009
Posts: 50544
Re: Triangle XYZ is an isosceles right triangle. If side XY is longer than  [#permalink]

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02 Feb 2015, 02:17
1
Bunuel wrote:
Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 16, what is the measure of side XY?

A. 4
B. 4√2
C. 8
D. 8√2
E. Cannot be determined from the information provided

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

While the stimulus doesn't seem to contain a ton of information, the terms "isosceles" and "right" that define the triangle make that one value (Area = 16) go a long way. Since you know that XY is longer than YZ, then XY must be the hypotenuse and sides YZ and XZ must be the shorter sides. Meaning, also that side XY will be equal to side YZ√2.

With an isosceles right triangle, you also know that the area (which here is 16) is equal to 1/2*(shorterside)^2. So that means that here 16=1/2*s^2 and that one of the shorter sides then measures 4√2. Since the hypotenuse, then is s√2, you'll multiply 4√2(√2) to find that side XY measures 8.
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Re: Triangle XYZ is an isosceles right triangle. If side XY is longer than  [#permalink]

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03 Feb 2015, 20:21
2
Refer diagram below:

Attachment:

tri.png [ 1.85 KiB | Viewed 5710 times ]

We require to find hypotenuse XY of the triangle

Area $$= \frac{1}{2} a^2 = 16$$

a $$= 4\sqrt{2}$$

XY $$= \sqrt{(4\sqrt{2})^2 + (4\sqrt{2})^2} = \sqrt{64} = 8$$
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Re: Triangle XYZ is an isosceles right triangle. If side XY is longer than  [#permalink]

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09 Sep 2018, 23:45
Bunuel wrote:
Triangle XYZ is an isosceles right triangle. If side XY is longer than side YZ, and the area of the triangle is 16, what is the measure of side XY?

A. 4
B. 4√2
C. 8
D. 8√2
E. Cannot be determined from the information provided

Kudos for a correct solution.

In an isosceles right triangle, the two legs are equal in length and the hypotenuse is sqrt(2) times the length of the legs. If the side XY is longer than side YZ, XY must be the hypotenuse.

Area of isosceles right triangle $$= (1/2)*side^2 = 16$$
$$Side = 4\sqrt{2}$$

Hypotenuse $$XY = \sqrt{2}*4\sqrt{2} = 8$$

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Re: Triangle XYZ is an isosceles right triangle. If side XY is longer than &nbs [#permalink] 09 Sep 2018, 23:45
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# Triangle XYZ is an isosceles right triangle. If side XY is longer than

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