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# If XZ is double AC, then the area of triangle XYZ is how many times gr

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Math Expert
Joined: 02 Sep 2009
Posts: 53004
If XZ is double AC, then the area of triangle XYZ is how many times gr  [#permalink]

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17 Jan 2019, 22:49
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:16) correct 27% (01:12) wrong based on 43 sessions

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If XZ is double AC, then the area of triangle XYZ is how many times greater than the area of triangle ABC?

A √2
B 2
C 4
D 8
E 16

Attachment:

2019-01-18_1047.png [ 7.41 KiB | Viewed 289 times ]

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Re: If XZ is double AC, then the area of triangle XYZ is how many times gr  [#permalink]

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18 Jan 2019, 05:15
Bunuel wrote:

If XZ is double AC, then the area of triangle XYZ is how many times greater than the area of triangle ABC?

A √2
B 2
C 4
D 8
E 16

Attachment:
2019-01-18_1047.png

let ac= sqrt 2 xz= 2swrt 2
area would 2 and other would 1/2
so 2/1/2 = 4
IMO C
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Joined: 15 Feb 2018
Posts: 244
Re: If XZ is double AC, then the area of triangle XYZ is how many times gr  [#permalink]

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19 Jan 2019, 00:38
1
a 45-45-90 triangle is isosceles. Two sides are of equal length (denote with x). The hypotenuse is x√2 long.

One triangle can have 2·2·2√2
The larger triangle has a hypotenuse of 2·2√2=4√2. Thus, its two other sides are both of length 4

Area of a triangle is 0.5·base·height
0.5·2·2=2
0.5·4·4=8
8/2=4

C
Re: If XZ is double AC, then the area of triangle XYZ is how many times gr   [#permalink] 19 Jan 2019, 00:38
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