If the area of a square field is x2 + y2 + z2 + 2xy – 2yz – 2zx sq. units, then its perimeter is
A) (x + y + z)2
B) 4 (x + y + z)
C) 4 (x + y – z)
D) (x + y – z)2
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Correct option is (C) 4 (x + y – z)
Let side length of the square be a unit.
\(\therefore a^2=x^2+y^2+z^2+2xy-2yz-2zx\)
\(=x^2+y^2+(-z)^2+2\times x\times y\) \(+2\times y\times -z+2\times -z\times x\)
\(=(x+y-z)^2\) sq. units
\(\Rightarrow\) \(a=(x+y-z)\) unit
\(\therefore\) Perimeter of the square = 4a
= \(4\,(x+y-z)\) unit
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