The perimeter of a rectangle is 42 m. If the length is 6 less than twice the width, find the length and width.

Answer 1

a = length

b = width

2*(a+b) = 42

a + b = 21

a = 2b -6

a + b = 21

(2b - 6) + b = 21

3b - 6 = 21

3b = 21 + 6 = 27

b = 9

a = 21 - b = 21 - 9 = 12

a = 12, b = 9

Answer 2

Here's what we know:

P = 2L + 2w (the preimeter of a rectangle is the two lengths and two widths added together.)

L = 2w - 6 (the length is 6 less than twice the width)

P = 42 (the perimeter is 42 meters around)

Let's plug in the values into the equation:

42 = 2(2w - 6) + 2w

Now to solve for width. Distribute:

42 = 4w - 12 + 2w

simplify:

42 = 6w - 12

Add 12 to both sides:

54 = 6w

Divide both sides by 6:

9 = w

Now to find the length:

L = 2 * 9 - 6

L = 18 - 6

L = 12

check:

42 = 12 * 2 + 9 * 2

42 = 24 + 18

42 = 42