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# ZW has a length of 3 and XZ has a length of 6. What is the area of tri

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Joined: 02 Sep 2009
Posts: 58445
ZW has a length of 3 and XZ has a length of 6. What is the area of tri  [#permalink]

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19 Dec 2018, 01:06
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Difficulty:

15% (low)

Question Stats:

94% (01:15) correct 6% (02:20) wrong based on 36 sessions

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ZW has a length of 3 and XZ has a length of 6. What is the area of triangle XYZ?

A. 8
B. 9
C. 10
D. 11
E. 12

Attachment:

Capture (4).JPG [ 18.66 KiB | Viewed 452 times ]

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Re: ZW has a length of 3 and XZ has a length of 6. What is the area of tri  [#permalink]

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19 Dec 2018, 06:44
Bunuel wrote:

ZW has a length of 3 and XZ has a length of 6. What is the area of triangle XYZ?

A. 8
B. 9
C. 10
D. 11
E. 12

Attachment:
Capture (4).JPG

20s:

Find area of entire triangle - area of small.

Area of entire:
B*H /2= (6+3)*h. Notice 3-4-5 triangle. H=4.
9*4/2=18

Area of small:
3*4/2=6

18-6=12
E IMO
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Re: ZW has a length of 3 and XZ has a length of 6. What is the area of tri  [#permalink]

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19 Dec 2018, 07:00
Bunuel wrote:

ZW has a length of 3 and XZ has a length of 6. What is the area of triangle XYZ?

A. 8
B. 9
C. 10
D. 11
E. 12

Attachment:
Capture (4).JPG

Area of triangle XYZ = (1/2) * Base * Altitude

Altitude = YW = 4 (since ZYW is a right triangle of pythagorean triplet 3-4-5)

Area of triangle XYZ = (1/2) * 6 * 4 = 12
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ZW has a length of 3 and XZ has a length of 6. What is the area of tri  [#permalink]

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19 Dec 2018, 07:00
2
Question : Area of Triangle XYZ .?

Given : ### ZW = 3; XZ = 6;
So, XW = 9
### Triangles ZYW & XYW are Right Angled Triangles
So by Pythagorean Triplets 3-4-5 in Triangle ZYW we have YW = 4

Now,
Area of Triangle XYZ = Area of Triangle XYW - Area of Triangle ZYW

In Triangle XYW ==> Base (XW) = 9 ; Height (YW) = 4 ; Therefore Area of XYW = 18
In Triangle ZYW ==> Base (ZW) = 3 ; Height (YW) = 4 ; Therefore Area of ZYW = 6

So,
Area of Triangle XYZ = Area of Triangle XYW - Area of Triangle ZYW
= 18 -6
ZW has a length of 3 and XZ has a length of 6. What is the area of tri   [#permalink] 19 Dec 2018, 07:00
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