Question

the length of a rectangle is 3 units shorter than one -third of the width, x. Which expression represents the perimeter of the rectangle? A) 8/3x-6, B) 2/3x -4, C) 2/3x -8, D) 8/3x -2.​

Answer 1

A)
`(8)/(3) x - 6`

Explanation:

Let the width of the rectangle be x units.

`\therefore \: length \: of \: rectangle = (1)/(3) x - 3 \\ Perimeter \: of \: rectangle = 2(l + w) \\ = 2 \bigg( (1)/(3) x - 3 + x \bigg)\\ = 2 \bigg( x + (1)/(3) x - 3 \bigg)\\ = 2 \bigg( (3x + x)/(3) - 3 \bigg)\\ = 2 \bigg( (4x)/(3) - 3 \bigg) \\ = 2 \bigg( (4x)/(3) - 3 \bigg) \\ = (2 * 4x)/(3) -2 * 3 \\ \purple{ \bold{{Perimeter \: of \: rectangle = (8)/(3) x - 6}}}`