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

Answer:

A) $\frac{8}{3} x - 6$

Step-by-step explanation:

Let the width of the rectangle be x units.

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