If the area of a square field is x2 + y2 + z2 + 2xy – 2yz – 2zx sq

1.	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
Answer» 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 C) 4 (x + y – z)

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

Answer»

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

C) 4 (x + y – z)