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(3) Determine the value of
x so that the square and the rectangle shown have equal perimeters

( $3$ ) Determine the value of $x$ so that the square and the rectangle shown have equal perimeters

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Find the magnitude of a three-dimensional vector

Full solution

Q. (

3

) Determine the value of

x

so that the square and the rectangle shown have equal perimeters

Calculate Square Perimeter: Square side length is given as $5$ cm, so its perimeter $P_{\text{square}} = 4 \times \text{side} = 4 \times 5 = 20$ cm.
Calculate Rectangle Perimeter: Rectangle lengths are given as $x$ cm and $(x + 2)$ cm, so its perimeter $P_{\text{rectangle}} = 2 \times (x + x + 2) = 2 \times (2x + 2)$ .
Set Perimeters Equal: Set the perimeters equal to each other: $P_{\text{square}} = P_{\text{rectangle}}$ , so $20 = 2 \times (2x + 2)$ .
Solve for x: Solve for x: $20 = 4x + 4$ .
Subtract $4$ : Subtract $4$ from both sides: $20 - 4 = 4x$ , so $16 = 4x$ .
Divide by $4$ : Divide both sides by $4$ : $16 / 4 = x$ , so $x = 4$ .

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