Question

please answer this is emergency ​

Answer 1

Given: A rectangle is constructed using 6 squares, each having a side equal to x m.

To Find: An algebraic expression for the area and the perimeter of the   rectangle.  

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Rectangle using 6 squares can be formed in 2 ways

$\boxed{\sf 1 \times 6 \; or \; 2 \times 3 }$  

FIGURE: Attached.

Therefore, solving for both case,

 

$\underline{\frak{\dag \; Case \; 1:}}$

$\sf 1 \times 6$

 

$:\implies \sf Length = 6x \\\\:\implies \sf Width = x \\\\:\implies \sf Area = 6x.x = 6x^2 \\\\:\implies \sf Perimeter = 2(x + 6x) \\\\:\implies \underline{\boxed{\frak{\pink{ Perimeter = 14x}}} }\; \bigstar$

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$\underline{\frak{\dag \; Case \; 2:}}$

$\sf 2 \times 3$

$:\implies \sf Length = 3x \\\\:\implies \sf Width = 2x \\\\:\implies \sf Area = 3x.2x = 6x^2 \\\\:\implies \sf Perimeter = 2(3x + 2x) \\\\:\implies \underline{\boxed{\frak{\pink{ Perimeter = 10x}} }} \; \bigstar$

$\therefore \sf{\underline{An \; algebraic \; equation \; for \; the \; perimeter \; of \; rectangle \; are \; 14x \; \& \; 10x}}$