Final answer:
To determine the length and width of the sandbox, define a variable, represent the width as w, and the length as w + 3, then use the perimeter formula P = 2l + 2w to create the equation 2(w + 3) + 2w = 62. Solve for w to find the dimensions.
Step-by-step explanation:
To find the length and width of the child's rectangular sandbox with a perimeter of 62 feet where the length is three feet longer than the width, let us define a variable, w, to represent the width of the sandbox in feet. The length would then be w + 3 feet. The formula for the perimeter (P) of a rectangle is P = 2l + 2w, where l is the length and w is the width.
By substituting the expressions for length and width into the perimeter formula, we obtain the equation 2(w + 3) + 2w = 62. Simplifying this, we get 2w + 6 + 2w = 62, which further simplifies to 4w + 6 = 62. Then, we subtract 6 from both sides to get 4w = 56. Finally, divide both sides by 4 to find the width, w = 14 feet. The length can then be determined by adding 3 to the width, resulting in l = 17 feet.