Question

The length of a rectangle is 3 centimeters less than twice its width. The perimeter of the rectangle is 48 cm. What are the dimensions of the rectangle?
A)length = 15 cm; width = 9 cm
(B)length = 11 cm; width = 7 cm
(C)length = 12 cm; width = 12 cm
(D)length = 14 cm; width = 10 cm

Answer 1

Let the width be w, then the length is 2w - 3
Perimeter = 2(length + width)
48 = 2(2w - 3 + w) = 2(3w - 3)
3w - 3 = 48/2 = 24
3w = 24 + 3 = 27
w = 27/3 = 9 cm

Therefore, width is 9 cm and the length is 2(9) - 3 = 18 - 3 = 15 cm

Answer 2

The equation for the length is L=2W - 3. The perimeter is 48 cm and the equation for finding the perimeter is P = 2W + 2L. Substitute the formula of L into the formula for perimeter and solve algebraically:

$P = 2W +2L \\ 48= 2W + 2(2W-3) \\ 48=2W + 4W - 6 \\ 48 = 6W - 6 \\ 48+6 = 6W \\ 54=6W \\ W=9 \\ L=2(9)-3 = 15$

The correct answer is A) length = 15cm; width = 9cm