Answer:
To find the length and width of the rectangle, we need to set up an equation using the given information.
The perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 42 meters.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Let's substitute the given expressions for the length and width into the formula:
42 = 2(12x+5 + 14x+4)
Simplifying the equation, we have:
42 = 2(26x + 9)
Now, let's distribute the 2:
42 = 52x + 18
To solve for x, we can subtract 18 from both sides of the equation:
42 - 18 = 52x
24 = 52x
To isolate x, we can divide both sides of the equation by 52:
x = 24/52
Simplifying the fraction, we get:
x = 6/13
Now that we have the value of x, we can substitute it back into the expressions for the length and width:
Length = 12x + 5
Length = 12(6/13) + 5
Simplifying the expression, we get:
Length = 72/13 + 5
To add the fractions, we need a common denominator of 13:
Length = (72 + 65)/13
Length = 137/13
Width = 14x + 4
Width = 14(6/13) + 4
Simplifying the expression, we get:
Width = 84/13 + 4
To add the fractions, we need a common denominator of 13:
Width = (84 + 52)/13
Width = 136/13
So, the length of the rectangle is 137/13 meters and the width is 136/13 meters.