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In the figure above, three squares and a triangle have areas of A, B,

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In the figure above, three squares and a triangle have areas of A, B,  [#permalink]

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New post 09 Jan 2019, 02:01
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A
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E

Difficulty:

  25% (medium)

Question Stats:

85% (00:52) correct 15% (01:46) wrong based on 33 sessions

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In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36


Attachment:
2019-01-09_1359.png
2019-01-09_1359.png [ 41.05 KiB | Viewed 268 times ]

Attachment:
2019-01-09_1402.png
2019-01-09_1402.png [ 23.49 KiB | Viewed 358 times ]

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Re: In the figure above, three squares and a triangle have areas of A, B,  [#permalink]

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New post 09 Jan 2019, 03:17
Bunuel wrote:
Image
In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36


Attachment:
2019-01-09_1359.png

Attachment:
2019-01-09_1402.png



A=12
B= 9
C= 15

triangle X : 3:4:5
9:12:15
so 0.5*9*12 = 54 IMO D
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Re: In the figure above, three squares and a triangle have areas of A, B,  [#permalink]

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New post 09 Jan 2019, 06:54
Bunuel wrote:
Image
In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36


Attachment:
2019-01-09_1359.png

Attachment:
2019-01-09_1402.png


Since A, B and C are squares with area as 144, 81 and 225, the side in each case is 12, 9 and 15. Note that the sides are in the ratio 3:4:5.
So X must be a right triangle.
Area X = (1/2)*12*9 = 54

Answer (D)
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Re: In the figure above, three squares and a triangle have areas of A, B,  [#permalink]

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New post 09 Jan 2019, 10:00
Bunuel wrote:
Image
In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36


Attachment:
2019-01-09_1359.png

Attachment:
2019-01-09_1402.png


Since each rectangle is stated to be a square, the sides of A B and C are 12,9 and 15 respectively. Since these values are in the ratio 3:4:5, the triangle must be a right triangle, therefore the lengths of A and B will be our length and our height. A=1/2 *B*h = 1/2 (12*9) = (1/2)(108) = 64 (D)
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Re: In the figure above, three squares and a triangle have areas of A, B,  [#permalink]

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New post 09 Jan 2019, 10:49
Since Area of square A=144, side of A=12
Since Area of square B=81,side of B= 9
Since Area of square C= 225,side of C=15

Now, in triangle X :
Sides are 9,12,15 which shows that the sides are in ratio of 3:4:5
Hence Triangle X is a right angled triangle.

so area of triangle X= 0.5*9*12 = 54
IMO D
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Re: In the figure above, three squares and a triangle have areas of A, B,  [#permalink]

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New post 09 Jan 2019, 11:33
Bunuel wrote:
Image
In the figure above, three squares and a triangle have areas of A, B, C, and X as shown. If A = 144, B = 81, and C = 225, then X =

(A) 150
(B) 144
(C) 80
(D) 54
(E) 36


Attachment:
2019-01-09_1359.png

Attachment:
2019-01-09_1402.png


The size of the boxes is actually part of the proof for pythagoras' theorem, so if you recognized that this question was easy!
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Re: In the figure above, three squares and a triangle have areas of A, B, &nbs [#permalink] 09 Jan 2019, 11:33
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