Answer:
Perimeter = 72 meters
Step-by-step explanation:
Let L be the length and W the width of the rectangle
We have the following relationship
L = 2W + 6
Area of the rectangle = LW = (2W+6)W by substituting for L
Area =
2W² + 6W =260 ==> 2W² + 6W -260 = 0
Dividing both sides by 2 yields
W² + 3W -130 = 0
This is a quadratic equation which can be solved using the formula for the roots of the equation ie the values of W which satisfy the above equation
However in this case it is easier to solve by factorization
W² + 3W -130
= W² + 13W - 10W - 130
= W(W + 13) -10(W + 13)
= (W+13)(W-10) = 0
This means W is either -13 or W = 10
Since W cannot be negative, we get W = 10 and
L = 2(10) + 6 = 26
Perimeter of a rectangle is given by
2(L + W) = 2(26 + 10) = 2(36) = 72 Answer
