Question

The length of a rectangle is 6 inches more than 3 times the width. The perimeter is 100 inches. Find the length and the width.

Answer 1

length = 39 inches

width = 11 inches

Explanation:

Assuming the length of the rectangle to be l and width to be w, we can write the length as:

`l = 3 w + 6`

We know that perimeter of the rectangle is 100 inches and its formula is:

Perimeter of a Rectangle = 2l + 2w

So substituting the given values in the above formula:

`100 = 2l+2w`

`100=2(3w+6)+2w`

`100=6w+12+2w`

`8w=100-12`

`8w=88`

`w=11`

Substituting this value of w to find the length l:

`l=3(11)+6\\\\l=33+6\\\\l=39`

Therefore, the length = 39 inches and width = 11 inches.

Answer 2

The width is 11 inches

The length is 39 inches

Explanation:

Length of a rectangle is 6 inches more than 3 times the width

l= 3w+6

Perimeter is 100 inches

P = 2(l+w)

100 = 2(l+w)

Substitute in for l

100 =2(3w+6 +w)

Combine like terms

100 =2(4w+6)

Divide each side by 2

100/2 = 2/2 (4w+6)

50 = 4w+6

Subtract 6 from each side

50-6 =4w+6-6

44 = 4w

Divide by 4

44/4 = 4w/4

11 =4

The width is 11 inches

Now we need to find the length

l= 3w+6

l= 3(11)+6

l = 33+6

l = 39 inches