Question

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 her scarf?​

Answer 1

To find the dimensions of Marianne's scarf, we set up a quadratic equation with the width as 'w' and solved to determine the width is 7 inches and the length is 12 inches.

Step-by-step explanation:

The students question involves finding the dimensions of Marianne's scarf given that the scarf's length is 5 inches longer than its width and that it has an area of 84 square inches. We can set up an equation to solve this problem.

Let's denote the width of the scarf as w inches. Then, the length of the scarf would be w + 5 inches. We know that Area = Length × Width, so we can write the equation:

84 = w × (w + 5)

To solve for w, we need to find the values of w that satisfy the equation, which is a quadratic equation that can be solved by factoring, completing the square, or using the quadratic formula. After solving, we get that the width of the scarf is 7 inches and the length is 12 inches.

Answer 2

The dimensions of Marianne scarf = 12 × 7 inches

The length of the scarf =12inches

The width of the scarf = 7 inches

Step-by-step explanation:

Step(i):-

Let 'x' be the width of the scarf

Given that the length of the scarf = x+5

The area of the rectangle = length × width

Given that the area of the rectangle (scarf) = 84 square inches

Step(ii):-

length × width = 84

(x+5) × x = 84

x² + 5x - 84 =0

x² + 12 x - 7 x - 84 =0

x(x+12) -7( x+12) =0

(x-7)(x+12) =0

x -7 =0 and x+12=0

x =7 and x= -12

Step(iii):-

We have to choose x =7

The length of the scarf = x+5 = 7+5 =12inches

The width of the scarf = x = 7 inches