Question

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 1

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

Answer 2

C) 4 (x + y – z)