Final answer:
The width of the rectangle is 12 cm and the length is 31 cm.
Step-by-step explanation:
Let's represent the width of the rectangle as w. According to the problem, the length of the rectangle is 7 cm more than twice the width, so we can express the length as 2w + 7. The formula for the perimeter of a rectangle is P = 2(l + w), where l is the length and w is the width. In this case, the perimeter is given as 86 cm. Plugging in the values into the formula, we get:
86 = 2((2w + 7) + w)
Simplifying the equation:
86 = 2(3w + 7)
86 = 6w + 14
72 = 6w
w = 12
Substituting the value of w back into the expression for the length:
l = 2w + 7 = 2(12) + 7 = 31
Therefore, the dimensions of the rectangle are 12 cm by 31 cm.