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If ABCD is a rectangle, then what is the area of triangle ALC?

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Bunuel
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If ABCD is a rectangle, then what is the area of triangle ALC? [#permalink] New post   08 Apr 2020, 10:57
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E

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Question Stats:

80% (01:27) correct 20% (01:33) wrong based on 116 sessions
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If ABCD is a rectangle, then what is the area of triangle ALC?

A. 2.5
B. 3
C. 3.5
D. 4
E. 4.5


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E
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Re: If ABCD is a rectangle, then what is the area of triangle ALC? [#permalink] New post   08 Apr 2020, 11:33
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Bunuel wrote:

If ABCD is a rectangle, then what is the area of triangle ALC?

A. 2.5
B. 3
C. 3.5
D. 4
E. 4.5


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GRE Math Q1.png


∆ ADL = 3:4:5 ; AREA = 1/2*3*4 = 6
AND ∆ ABC = 1/2 * 7*3= 11.5
rectangle area= 7*3 =21
∆ALC = 21-(6+11.5) ; 4.5
OPTION E
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Re: If ABCD is a rectangle, then what is the area of triangle ALC? [#permalink] New post   11 Apr 2020, 06:13
ABCD is a rectangle, hence angle ADL is a right angle and triangle ADL is a right angled triangle.
In triangle ADL, hypotenuse = AL = 5 and leg = AD = 3. Therefore, DL = base = 4.

ABCD is a rectangle, therefore AB = DC = 7

DC = DL + LC, so 7 = 4 + LC which gives us LC = 3.

Area of triangle ALC = ½ X LC X AD {since AD is the height of the triangle ALC} = ½ X 3 X 3 = 4.5 sq.units.
The correct answer option is E.

Remember – if the base of a triangle lies on one of the lengths of a rectangle and the third vertex lies on the other length, the width of the rectangle represents the height of the triangle.

Hope that helps!
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If ABCD is a rectangle, then what is the area of triangle ALC? [#permalink] New post   12 Apr 2020, 02:13
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Solution



Given
In this question, we are given that
    • ABCD is a rectangle

To find
We need to determine
    • The area of the triangle ALC

Approach and Working
As ABCD is a rectangle, each of the angles of the rectangle is 90
    • Thus, we can infer that both ADL and ACB are right-angle triangles (as angle ADL = angle ABC = 90)

Considering triangle ADL, AD = 3 and AL = 5.
    • Hence, following the Pythagorean triplet of 3-4-5, we can infer that DL = 4
    • So, area of triangle ADL = ½ x AD x DL = ½ x 3 x 4 = 6

Similarly, considering triangle ACB, AB = 7 and BC = AD = 3
    • So, area of triangle ACB = ½ x AB x BC = ½ x 7 x 3 = 10.5

From the given diagram, we can also visualise that
    • Area of triangle ADL + area of triangle ALC + area of triangle ACB = area of rectangle ABCD = 3 x 7 = 21
    Or, 6 + ALC + 10.5 = 21
    Or, ALC = 21 – 6 – 10.5
    Or, ALC = 4.5

Thus, option E is the correct answer.

Correct Answer: Option E

For more details on the terms "Infer" and "Visualize", click on the image below



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Re: If ABCD is a rectangle, then what is the area of triangle ALC? [#permalink] New post   29 Nov 2021, 15:15
Area (ALC) = ABCD - ADL - ABC
ABCD = 3*7 = 21
ADL is a 3, 4, 5 right triangle, so ADL = .5*3*4 = 6
ABC = .5*7*3 = 10.5
ALC = 21-6-10.5 = 4.5
Ans = E
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Re: If ABCD is a rectangle, then what is the area of triangle ALC? [#permalink]
29 Nov 2021, 15:15
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