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# In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet.

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In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet.  [#permalink]

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05 Feb 2019, 03:29
00:00

Difficulty:

25% (medium)

Question Stats:

88% (01:51) correct 12% (01:46) wrong based on 17 sessions

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In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet?

A. xy/2 + 2

B. xy/2 - x - y - 2

C. xy/2 - x - y + 2

D. xy - 2x - 2y - 4

E. xy - 2x - 2y + 4

Attachment:

2019-02-05_1527.png [ 12.52 KiB | Viewed 254 times ]

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Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet.  [#permalink]

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05 Feb 2019, 03:55
Length of DE = x-2
Length of DF = y-2
Area of triangle = 1/2*(x-2)*(y-2)

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Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet.  [#permalink]

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05 Feb 2019, 05:00
Bunuel wrote:

In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet?

A. xy/2 + 2

B. xy/2 - x - y - 2

C. xy/2 - x - y + 2

D. xy - 2x - 2y - 4

E. xy - 2x - 2y + 4

Attachment:
2019-02-05_1527.png

DF= x-2
DE= y-2
area of triangle = 1/2 * ( x-2) * ( y-2)
upon solving
xy/2 - x - y + 2
IMO C
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Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet.  [#permalink]

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06 Feb 2019, 18:45
Bunuel wrote:

In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet?

A. xy/2 + 2

B. xy/2 - x - y - 2

C. xy/2 - x - y + 2

D. xy - 2x - 2y - 4

E. xy - 2x - 2y + 4

Attachment:
2019-02-05_1527.png

Side ED = y - 2 and side DF = x - 2, so the area of triangle DEF is:

(y - 2)(x - 2) x 1/2

(xy - 2x - 2y + 4) x 1/2

xy/2 - x - y + 2

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Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet.  [#permalink]

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06 Feb 2019, 18:57
Bunuel wrote:
In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet. What is the area of triangle DEF, in square feet?

A. xy/2 + 2

B. xy/2 - x - y - 2

C. xy/2 - x - y + 2

D. xy - 2x - 2y - 4

E. xy - 2x - 2y + 4

Attachment:
2019-02-05_1527.png

So just plot the expressions for the triangle

ED =y -2
DF = x -2

Its a rectangle all angles are $$90^o$$

Area of triangle DEF = 1/2 * y-2 * x-2

xy/2 - x - y + 2
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Re: In the rectangle above, AB = x feet,BC = y feet, and AE = FC = 2 feet.   [#permalink] 06 Feb 2019, 18:57
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