Answer :
The equation that can be used to determine the area of the double blanket is:
D = [tex]W^2 + 24W + 1,260[/tex]
Variable we are using here are as follows
W: Width of twin blanket (inches), L: Length of both blankets (inches), D: Area of double blanket (square inches)
We are given information about the sizes and areas of two blankets: the twin and the double. We need to find an equation to determine the area of the double blanket.
Identifying variables: We need to define variables to represent the dimensions of the blankets. Let:
W: Width of the twin blanket (in inches)
L: Length of the twin blanket (in inches) (same for both blankets)
D: Area of the double blanket (in square inches)
Relating variables: We know that the twin blanket is 24 inches longer than it is wide, so:
L = W + 24
Area of the twin blanket: The area of a rectangle is calculated by multiplying its length and width. So, the area of the twin blanket (T) is:
T = W × L = W × (W + 24)
Difference in area: We are also given that the area of the twin blanket is 1,260 square inches less than the area of the double blanket. This can be expressed as:
D - T = 1,260
Substituting expressions: We can substitute the expression for the twin blanket area (T) into the equation for the difference in area:
D - (W × (W + 24)) = 1,260
Simplifying and rearranging: Expanding the parentheses and rearranging the equation to isolate D, we get:
D = [tex]W^2 + 24W + 1,260[/tex]
