Question

Find the length of the rectangle if it's area is 22cm^2.
L=x-2
W=x-11

Answer 1

To find the length of the rectangle, we can use the formula for the area of a rectangle, which is length times width. Since the area is given as 22cm^2, we can set up the equation:

(L)(W) = Area
(x-2)(x-11) = 22
x^2 - 11x - 2x + 22 = 0
x^2 - 13x + 22 = 0

Now we need to find two numbers that multiply to 22 and add up to -13. The numbers are -11 and -2:

(x - 11)(x - 2) = 0

This gives us two possible values for x: x = 11 or x = 2. Since the length is given by L = x - 2, we can substitute these values back in to find the lengths:

For x = 11:
L = 11 - 2
L = 9

For x = 2:
L = 2 - 2
L = 0

Since the length of a rectangle cannot be zero, the length is 9 cm.