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Retired Moderator V
Joined: 27 Oct 2017
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WE: General Management (Education)
In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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Question Stats: 92% (01:11) correct 8% (01:01) wrong based on 37 sessions

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GMATBusters’ Quant Quiz Question -6 In the diagram above, triangle CDE is inscribed in square ABCD. If the area of the triangle is 50, what is the perimeter of the square?
A. 20
B. 32
C. 40
D. 48
E. 50

Attachment: gc1.JPG [ 16.26 KiB | Viewed 478 times ]

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Director  P
Joined: 14 Dec 2019
Posts: 673
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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Area of triangle = \frac{1}{2}*CD*AC = 50 => CD*AC = 100

Since CD = AC (as they are sides of a square)

CD = AC = 10

Therefore Perimeter = 4*CD = 40 - Answer - C
Director  V
Joined: 22 Feb 2018
Posts: 780
Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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In the diagram above, triangle CDE is inscribed in square ABCD. If the area of the triangle is 50, what is the perimeter of the square?

Area of triangle CDE = 50,
1/2 * CD * EO = 50 (if we assume point O, which is perpendicular, on CD)
So, CD * EO = 100
CD = 10 and EO = 10 as EO is length of square.
So, length of square = 10 each. So perimeter of square = 40.

Ans. C
CEO  V
Joined: 03 Jun 2019
Posts: 3182
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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In the diagram above, triangle CDE is inscribed in square ABCD. If the area of the triangle is 50, what is the perimeter of the square?
A. 20
B. 32
C. 40
D. 48
E. 50

Let the side of the square ABCD be x

Area of triangle CDE = 1/2 * CD * AC = x^2/2 = 50
x^2 = 100
x = 10

Perimeter of the square ABCD = 4*10 = 40

IMO C
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Kinshook Chaturvedi
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Joined: 12 Nov 2017
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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As ABCD is a square AB=BC=CD=DA=x
Assume a line EF, perpendicular to line CD
Where EF=x
Now area of the triangle 1/2. EF.CD=50
EF.CD=100
x2=100
x=10

So the perimeter of the square is, 4x=40

Ans. C
Intern  B
Joined: 02 Dec 2019
Posts: 10
Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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In the diagram above, triangle CDE is inscribed in square ABCD. If the area of the triangle is 50, what is the perimeter of the square?
A. 20
B. 32
C. 40
D. 48
E. 50

The area of the triangle is 1/2 * b * h. in this case, the base and height also = the side of the square
50 = 1/2 (s) (s) --> s = 10 --> perimeter = 40 --> answer is (c)
Manager  S
Joined: 14 Aug 2017
Posts: 68
Location: India
Concentration: Other, General Management
GMAT 1: 640 Q48 V29
Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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we just need to use the formula of the trangle . 1/2 base * height . we get side so 4 * side is the answer 40
Intern  B
Joined: 24 Mar 2019
Posts: 18
Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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Option (C)40
Area of triangle
=b×h/2
=CD×CA/2 (height has same length as CA, base is CD)
=CD^2/2 (CA=CD since it's a square)
= 50
CD = sqrt(100) = 10
Perimeter=4×CD=40

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LBS Moderator P
Joined: 30 Oct 2019
Posts: 477
Location: United Kingdom
Concentration: General Management, Technology
GPA: 4
Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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$$\triangle CDE = \frac{1}{2}*base*altitude = 50$$
$$or, \frac{1}{2} * a * a = 50,$$
or, a = 10

Therefore, 4a = 40 Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t   [#permalink] 29 Mar 2020, 06:05

# In the diagram above, triangle ADE is inscribed in square ABCD. If t  