The width of a rectangle is 11 inches less than its length. Find the dimensions of the rectangle if the area is 80 square inches.
Hmmm.
80=5*16
To solve this problem, we can use the formula for the area of a rectangle, which is length multiplied by width.
Let's assume that the length of the rectangle is L inches. According to the problem, the width is 11 inches less than the length, so we can express the width as L - 11 inches.
Given that the area of the rectangle is 80 square inches, we can set up the equation:
Area = Length × Width
80 = L × (L - 11)
To solve this equation, we need to multiply L by L - 11 and set it equal to 80:
L^2 - 11L = 80
Now, rearrange the equation to move all the terms to one side:
L^2 - 11L - 80 = 0
At this point, we have a quadratic equation. To solve it, we can factor it or use the quadratic formula. Let's use factoring:
(L - 16)(L + 5) = 0
Setting each factor equal to zero gives us two separate equations:
L - 16 = 0 or L + 5 = 0
Solving each equation gives us:
L = 16 or L = -5
We can now substitute these values back into the formula for the width:
Width = L - 11
For L = 16, the width is:
Width = 16 - 11
Width = 5
For L = -5, the width is:
Width = -5 - 11
Width = -16
Since measurements cannot be negative in this context, we discard the negative value for L. Hence, the dimensions of the rectangle are:
Length = 16 inches
Width = 5 inches