Marianne has a scarf that is 5 inches longer than it is wide. If the area of her scarf is 84 square inches, what are the dimensions of the scarf ?
Let's call the width of the scarf "x".
According to the problem, the length of the scarf is 5 inches longer than the width. Therefore, the length is:
x + 5
To find the area of the scarf, we use the formula:
Area = Length × Width
Substituting the expressions for length and width:
84 = (x + 5) × x
Expanding the brackets:
84 = x^2 + 5x
Rearranging the terms into a quadratic equation:
x^2 + 5x - 84 = 0
We can solve for x using the quadratic formula:
x = (-5 ± √(5^2 - 4×1×(-84))) / (2×1)
Simplifying:
x = (-5 ± √(361)) / 2
Ignoring the negative solution (since width cannot be negative), we get:
x = (-5 + 19) / 2 or x = (-5 - 19) / 2
x = 7 or x = -12
We ignore the negative solution again. Therefore, the width of the scarf is 7 inches.
To find the length, we use the expression we found earlier:
Length = x + 5 = 7 + 5 = 12
Therefore, the dimensions of the scarf are 7 inches by 12 inches.