the perimeter of a rectangle is 38 inches. the length is 5 less than three times the width. find the length and width of the rectangle.

Answer 1

P= 2L+2W

(Perimeter of the rectangle equals twice the length + twice the width, where L=Length and W=Width)

Given:

Perimeter = 38 inches

Length= 3W-5

Using the formula: P=2L+2W, we can substitute (3W-5 where we see L and 38 where we see P), so:

38= 2(3W-5)+2W

38= 6W-10+2W (we distributed the 2 across the 3W-5 in the parentheses)

38= 8W-10 (Simplifying the right side of the equation-- combining like terms)

48= 8W (Adding ten to both sides to start isolating the variable W on the right hand side)

6= W (Dividing by 8 on both sides to isolate the variable W)

Now that you know the width, "W", is equal to six, you can find the measure of the length by substituting 6 into the formula Given for length, "3W-5"

Length= 3W-5

Length= 3(6)-5

Length= 18-5

Length= 13

Perimeter= 38

Perimeter= 2L + 2W

38= 2(13) + 2(6)

38= 26 + 12

38= 38 (correct)