PS challenger 25/04

Square J has area of 64 and is contained within square K; square K is contained within square L. If the length of a side of square K is equal to the length of a diagonal of square J and the area of square L is less than the sum of the areas of square J and square K, which of the following could be the length of a side of square L?
a. 11
b. 13
c. 15
d. 17
e. 19

2 comments:

Abhi 3/5/09 5:23 AM  

Ans: (b)

Area(J) = 64
Length(J) = 8

Length (K) = sqrt(2)*length(J)
= sqrt(2) * 8 = 1.414 * 8 = 11.312

Since square L contains K, the length of L > 11.312 ... condition(1)

Area(J) + Area(K) = 8*8 + 11.312*11.312
= 196.

Hence Area(L) should be < 196 ... condition(2)

Only option (b) satisfies the 2 conditions.

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