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

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Retired Moderator
Joined: 27 Oct 2017
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In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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28 Mar 2020, 18:38
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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

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Director
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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28 Mar 2020, 18:51
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
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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28 Mar 2020, 21:19
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
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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28 Mar 2020, 21:25
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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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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28 Mar 2020, 22:37
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
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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28 Mar 2020, 22:55
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)
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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29 Mar 2020, 04:57
we just need to use the formula of the trangle . 1/2 base * height . we get side so 4 * side is the answer 40
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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29 Mar 2020, 05:56
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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Concentration: General Management, Technology
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Re: In the diagram above, triangle ADE is inscribed in square ABCD. If t  [#permalink]

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29 Mar 2020, 06:05
$$\triangle CDE = \frac{1}{2}*base*altitude = 50$$
$$or, \frac{1}{2} * a * a = 50,$$
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