Question

The area of the square is half the area of the rectangle find x.
Length of the rectangle = 2 (x+4) Width of the rectangle = (x-2)
A side of the square is x

Answer 1

$Length \:of \:the \: rectangle = 2(x+4)$

$Width \:of \:the \: rectangle = (x-2)$

$and \: side \:of \:the \: square = x$

/* According to the problem given */

$\pink{ Area \: of \:the \: square }$

$\blue{ = \frac{1}{2}(Area \:of \:the \: rectangle}$

$\implies (side)^{2} = \frac{1}{2} \times length \times width$

$\implies x^{2} = \frac{1}{2} \times [2(x+4)] \times (x-2)$

$\implies x^{2} = (x+4)(x-2)$

$\implies x^{2} = x(x-2) + 4(x-2)$

$\implies \cancel {x^{2} } =\cancel { x^{2}} - 2x + 4x - 8$

$\implies 0 = 2x - 8$

$\implies 2x = 8$

$\implies x = \frac{8}{2}$

$\implies x = 4$

Therefore.,

$\red{ Side \:of \:a \:square (x)} \green { = 4 \:units }$

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