Question

the length or a rectangle is 11 centimeters less than 4 times it width its area is 20 square centimeters find the dimension of the rectangle use formula aera = length*width the width is cm

Answer 1

Width = W
Length = 4W-11

Area = L*W = W(4W-11)

4W2 - 11W = 20
4W2 - 11W - 20 = 0

We can attempt to factor this by grouping:
Multiply the coefficient of the squared term .. 4 ..
by the constant -20... 4(-20) = -80
We need to see if there are factors of -80 that add to
the coefficient of the middle W term... -11.
The factors of -80 that add to -11 are 5(-16)

Replace -11W with -16W + 5W in our equation

4W2 - 16W + 5W - 20 = 0
4W(W-4) + 5(W-4) = 20
(4W+5)(W-4) = 0

Either 4W + 5 = 0 or W-4 = 0
4W = -5 W = 4
W = -4/5

Since the width cannot be a negative number
Our width is 4cm

The length is given by L = 4W-11
= 4(4)-11
= 16-11
= 5cm