What is the area of square ABCD ?

Question

(1) The length of the side of square ABCD is 2.

(2) For square EFGH, which has sides that are 6 longer than those of square ABCD, the ratio of the perimeter to the area is the reciprocal of the corresponding ratio for square ABCD.

fameatop · Answer

Answer is D
Statement 2
Lets say the side of square ABCD is x & side of square EFGH is x+6
 Ratio of Perimeter to area of Square EFGH= Ratio of area to the perimeter of ABCD 
 ---> LHS = RHS 
 -->  4(x+6)/(x+6)^2 = (x^2)/4x 
 --> 4/(x+6) = x/4
 -->  x^2 + 6x -16 = 0 
Solving above equation we get x = either 2 or -8. As side can't be negative, x = 2-----Sufficient.

Answer D

Hope its clear.

Carcass · Answer

sorry can you elaborate more clear ?? ok we have P/A ---> 4(x+6)/(x+6)^2 -----> the numerator cancel out and in the denominator we have (x+6) Then A/P is : x+6/4. How do you have a quadratic equation ??' Thanks

Bunuel · Answer

The ratio of  the perimeter to the area  for square square EFGH is  \frac{4(x+6)}{(x+6)^2}=\frac{4}{x+6} ;

The ratio of  the area to the perimeter  for square square ABCD is  \frac{x^2}{4x}=\frac{x}{4} ;

We are told that these values are equal, so  \frac{4}{x+6}=\frac{x}{4} . Cross-multiply:  16=x(x+6)  -->  x^2+6x-16=0  -->  x=2  or  x=-8 .

Hope it helps.

bumpbot · Answer

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What is the area of square ABCD ?

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