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555-605 Level|   Geometry|      
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Bunuel
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The lengths of the sides of rectangles ABCD and ABEF, shown above, ar 19 Jun 2020, 04:26
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25% (medium)

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72% (02:01) correct 28% (02:16) wrong based on 54 sessions

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The lengths of the sides of rectangles ABCD and ABEF, shown above, are integers (in cm). The area of ABCD is 20 cm^2 and the area of ABEF is 10 cm^2. What is the minimum possible perimeter of the rectangle CDFE in cm?

A. 12
B. 14
C. 20
D. 22
E. 26

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B
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dimri10
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The lengths of the sides of rectangles ABCD and ABEF, shown above, ar 19 Jun 2020, 06:04
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should be 14
===BA=EF
===BA*BC=20
===EF*BE=10
SOLVE and the leat integer value is 2 for EC or BE and 5 fot EF=BA TO THE SUM OF 14

1/2*20 IS NOT VALID SINCE IT MAKES ONE SIDE A FRACTION.
1*10 MAKES THE perimeter 22


***the big rectangle is 20- the little one which is 10, makes the area we are looking for 10.

10=1*10 =perimeter 22
10=2*5=perimter 14.
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The lengths of the sides of rectangles ABCD and ABEF, shown above, ar 19 Jun 2020, 10:34
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Bunuel

The lengths of the sides of rectangles ABCD and ABEF, shown above, are integers (in cm). The area of ABCD is 20 cm^2 and the area of ABEF is 10 cm^2. What is the minimum possible perimeter of the rectangle CDFE in cm?

A. 12
B. 14
C. 20
D. 22
E. 26

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For a given area, Square has a minimum perimeter
Here Area CDFE=10
side= \(\sqrt{10}\)
=3.1
Perimeter= 3.1*4
=12.64
B:)
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The lengths of the sides of rectangles ABCD and ABEF, shown above, ar 24 Jun 2020, 11:06
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CDFE area = 20-10= 10 cm^2
Length*Breadth of the CDFE=EC*CD = 10 cm^2

we are asked to find least value of of 2(EC+CD)

We know, Arithmetic Mean>= Geometric Mean

=> (EC+CD)/2 >= Square root of EC*CD

=> 2(EC+CD) >= 4*square root of 10.

Perimeter will be least when it is equal to 4*square root of 10.

Square root of 10 is greater than 3 and less than 4. Therefore answer will be between 12 and 16. We have one option. Mark B
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The lengths of the sides of rectangles ABCD and ABEF, shown above, ar 24 Jun 2020, 22:39
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Bunuel

The lengths of the sides of rectangles ABCD and ABEF, shown above, are integers (in cm). The area of ABCD is 20 cm^2 and the area of ABEF is 10 cm^2. What is the minimum possible perimeter of the rectangle CDFE in cm?

A. 12
B. 14
C. 20
D. 22
E. 26

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Key point to note: Lengths of the sides are integers -> this greatly reduces the possible combinations

Area of CDEF = 20-10 = 10 cm2

Let the length and width of CDEF be L and W respectively. Therefore, L*W=10. Moreover, both L and W are integers.
Possible combinations are:
L=1, W=10 --> perimeter=(1+10)*2=22
L=2, W=5 --> perimeter=(2+5)*2=14

Therefore, answer is B
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