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# In the rectangular coordinate system above, if the base of the triangl

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Math Expert
Joined: 02 Sep 2009
Posts: 52284
In the rectangular coordinate system above, if the base of the triangl  [#permalink]

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24 Aug 2018, 01:48
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Difficulty:

25% (medium)

Question Stats:

73% (01:12) correct 27% (00:59) wrong based on 37 sessions

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In the rectangular coordinate system above, if the base of the triangle is parallel to the x-axis what is the area of the triangle?

(1) b – f = 0 and a – e = –4
(2) f – d = –3 and c – e = –2

Attachment:

image010.gif [ 904 Bytes | Viewed 435 times ]

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In the rectangular coordinate system above, if the base of the triangl  [#permalink]

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24 Aug 2018, 03:13
Bunuel wrote:

In the rectangular coordinate system above, if the base of the triangle is parallel to the x-axis what is the area of the triangle?

(1) b – f = 0 and a – e = –4
(2) f – d = –3 and c – e = –2

Attachment:
image010.gif

We need the value of the following parameters in order to determine the area of a triangle:
a) Length of three sides
b) Length of base and height

St1:- b – f = 0 and a – e = –4
Only measure of base is known.
base=a+4-a=4 unit
Measure of height is in dark.
Insufficient.

St2:- f – d = –3 and c – e = –2
Only measure of height is known.
Height=f+3-f=3 unit
Measure of base is in dark.
Insufficient.

Combined, measure of both base and height is known. Area can be calculated. (For reference, combining st1 & 2, vertices of the triangle become Left(a,b),Right(a+4,b), Top(a+2,b+3) and the coordinate intersection of base and height is (a+2,b))
Sufficient.

Ans. (C)
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Re: In the rectangular coordinate system above, if the base of the triangl  [#permalink]

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25 Aug 2018, 10:16
Bunuel wrote:

In the rectangular coordinate system above, if the base of the triangle is parallel to the x-axis what is the area of the triangle?

(1) b – f = 0 and a – e = –4
(2) f – d = –3 and c – e = –2

Attachment:
image010.gif

(1) b – f = 0 and a – e = –4
given that the base is parallel to x axis

area = $$\frac{b * h}{2}$$
b= difference in x co ordinates = 4 ( a-e)
h=difference in y co ordinates = ?

insufficient

(2) f – d = –3 and c – e = –2
b= difference in x co ordinates = ?
h=difference in y co ordinates = f-d=3

insufficient.

using both the statements

area = $$\frac{4*3}{2}$$= 6
sufficient
C
Re: In the rectangular coordinate system above, if the base of the triangl &nbs [#permalink] 25 Aug 2018, 10:16
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