    Question

# There are three figures of areas x2,12x and z in the below figure. Figures A and C are squares while figure B is a rectangle, with length of one side as x. What should be the value of z so that all the 3 figures can be arranged to form a square of side (x +6)? A
16
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B
36
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C
18
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D
24
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Solution

## The correct option is B 36Using the algebraic identity (a+b)2=(a2+2ab+b2), we have (x+6)2=x2+12x+36....(1) Thus, 36 must be added to x2 and 12x to make to complete the square. In mathematical terms, we have x2+12x+z=(x+6)2 ⟹x2+2(x)(6)+z=(x+6)2 ⟹z=36...(Using (i)) Thus, the value of z so that all the 3 figures can be arranged to form a square of side (x +6) is 36.  Suggest Corrections  1      Related Videos   Solving QE by Completing the Square
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