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605-655 (Medium)|   Geometry|      
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shridhar786
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The rectangles shown above are similar and the ratio of the area of 01 Oct 2019, 04:24
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

63% (01:50) correct 37% (01:59) wrong based on 112 sessions

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The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24

(B) 36

(C) 48

(D) 72

(E) It cannot be determined from the information given
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D
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The rectangles shown above are similar and the ratio of the area of 01 Oct 2019, 07:47
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shridhar786
Attachment:
ps7.PNG
The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24

(B) 36

(C) 48

(D) 72

(E) It cannot be determined from the information given
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Since area are in ratio 1:4, the sides will be in ratio \(\sqrt{1}:\sqrt{4}\) or \(1:2\)..
so \(x:144=1:2...x=\frac{144}{2}=72\)...

D.. Ofcourse, we assume that the rectangles are drawn to scale and x is related to 144 and not 96..
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The rectangles shown above are similar and the ratio of the area of 01 Oct 2019, 08:14
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shridhar786
Attachment:
ps7.PNG
The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24

(B) 36

(C) 48

(D) 72

(E) It cannot be determined from the information given

Since area are in ratio 1:4, the sides will be in ratio \(\sqrt{1}:\sqrt{4}\) or \(1:2\)..
so \(x:144=1:2...x=\frac{144}{2}=72\)...

D.. Ofcourse, we assume that the rectangles are drawn to scale and x is related to 144 and not 96..
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Hi!!!
1. Similar ration criteria is also applicable to rectangles ?

2. Let x be breadth and y be length then x*y = 24*144
Therefore x can take any value and hence I went with E.
Kindly guide.
Regards

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The rectangles shown above are similar and the ratio of the area of 01 Oct 2019, 10:35
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Attachment:
ps7.PNG
The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24

(B) 36

(C) 48

(D) 72

(E) It cannot be determined from the information given
Show more

Applying proportionality between the two rectangles helps to find the answer.
In the larger rectangle the sides are in the ratio of 2:3. Similarly, sides of smaller rectangle should be in ratio of 2:3 considering 'x' proportional to 144.

Let the other side of smaller rectangle be 'y' so y:x = 2:3.

Now, x * y = 144 * \(\frac{96}{4}\)
\(x *\)\(\frac{2x}{3}\) = 36 * 96
\(x^2\) = 3 * 36 * \(\frac{96}{2}\)
\(x = \sqrt{3 * 36 * 48}\)
\(x = \sqrt{3 * 6 * 6 * 4 * 4 * 3}\)
x = 72

Answer (D).
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The rectangles shown above are similar and the ratio of the area of Updated on: 02 Oct 2019, 03:02
Originally posted by Kinshook on 01 Oct 2019, 11:00.
Last edited by Kinshook on 02 Oct 2019, 03:02, edited 1 time in total.
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shridhar786
Attachment:
ps7.PNG
The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24

(B) 36

(C) 48

(D) 72

(E) It cannot be determined from the information given
Show more

Since the rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\), ratio of length of the small rectangle and the big rectangle is \(\frac{1}{2}\),
x/144 = 1/2
x = 72

IMO D
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The rectangles shown above are similar and the ratio of the area of 01 Oct 2019, 16:17
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given
area of small rectangle/ area of large rectangle = 1/4
x/144=1/2
x=72
IMO D



shridhar786
Attachment:
ps7.PNG
The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24

(B) 36

(C) 48

(D) 72

(E) It cannot be determined from the information given
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The rectangles shown above are similar and the ratio of the area of 01 Oct 2019, 16:18
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Kinshook
please see highlighted part

Kinshook
shridhar786
Attachment:
ps7.PNG
The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24

(B) 36

(C) 48

(D) 72

(E) It cannot be determined from the information given

Since the rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\), ratio of length of the small rectangle and the big rectangle is \(\frac{1}{2}\),
x/144 = 1/2
x = 172

IMO D
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The rectangles shown above are similar and the ratio of the area of 06 Nov 2019, 07:51
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shridhar786
Attachment:
ps7.PNG
The rectangles shown above are similar and the ratio of the area of the small rectangle over the area of the big rectangle is \(\frac{1}{4}\). What is the value of x?

(A) 24
(B) 36
(C) 48
(D) 72
(E) It cannot be determined from the information given
Show more

Assuming that X is similar to the longer side, 144.

If they are similar then the ratio of their areas is equal to the ratio of their corresponding sides squared:

\(area/Area=side^2/Side^2…1/4=x^2/144^2…1/2=x/144…x=72\)

Ans. (D)
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The rectangles shown above are similar and the ratio of the area of 27 Nov 2020, 01:14
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