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# In the figure above, if ZV = 4, UZ = 5, and ZY = 15, what is the ratio

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
In the figure above, if ZV = 4, UZ = 5, and ZY = 15, what is the ratio  [#permalink]

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11 Sep 2018, 02:02
00:00

Difficulty:

25% (medium)

Question Stats:

94% (01:26) correct 6% (01:38) wrong based on 17 sessions

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In the figure above, if ZV = 4, UZ = 5, and ZY = 15, what is the ratio of the area of triangle XYZ to triangle UVZ?

A. 9 : 1
B. 7 : 2
C. 3 : 1
D. 4 : 3
E. 2 : 1

Attachment:

8294_image.png [ 6.32 KiB | Viewed 312 times ]

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Re: In the figure above, if ZV = 4, UZ = 5, and ZY = 15, what is the ratio  [#permalink]

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11 Sep 2018, 02:13
triangle XYZ to triangle UVZ are right angled triangle.

From Pythagoras theorem UV = 3

From triangle XYZ. YZ = 15.

Then Base XY becomes 9
Height XZ becomes 12 (From Pythagoras theorem)

ratio of the area of triangle XYZ to triangle UVZ becomes 12*9 : 3*4 = 9:1

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In the figure above, if ZV = 4, UZ = 5, and ZY = 15, what is the ratio  [#permalink]

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11 Sep 2018, 02:20
1
Bunuel wrote:

In the figure above, if ZV = 4, UZ = 5, and ZY = 15, what is the ratio of the area of triangle XYZ to triangle UVZ?

A. 9 : 1
B. 7 : 2
C. 3 : 1
D. 4 : 3
E. 2 : 1

Attachment:
8294_image.png

using similarity of triangle (AAA)
angle Z=Z, V=X ,and U=Y
both the triangles are similar.

$$\frac{(UZ)^2}{(ZY)^2}$$ = $$\frac{area of UVZ}{area of XYZ}$$ ( this is a property) =$$\frac{25}{225}$$= $$\frac{1}{9}$$ =A
In the figure above, if ZV = 4, UZ = 5, and ZY = 15, what is the ratio &nbs [#permalink] 11 Sep 2018, 02:20
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