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

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Math Expert
Joined: 02 Sep 2009
Posts: 64242
If ABCD is a rectangle, then what is the area of triangle ALC?  [#permalink]

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08 Apr 2020, 09:57
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Difficulty:

25% (medium)

Question Stats:

77% (01:26) correct 23% (01:39) wrong based on 44 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

Attachment:

GRE Math Q1.png [ 1.77 KiB | Viewed 488 times ]

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Re: If ABCD is a rectangle, then what is the area of triangle ALC?  [#permalink]

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08 Apr 2020, 10:33
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

Attachment:
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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Joined: 12 Apr 2019
Posts: 590
Re: If ABCD is a rectangle, then what is the area of triangle ALC?  [#permalink]

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11 Apr 2020, 05:13
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]

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12 Apr 2020, 01:13
1

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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If ABCD is a rectangle, then what is the area of triangle ALC?   [#permalink] 12 Apr 2020, 01:13

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

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