Question

the length of a rectangle is 3 meters less than twice the width if the area is 104 square meters find the length

Answer 1

l = 13 m

Explanation:

Let's call the width of the rectangle x. Then we can form an expression for the length of the rectangle: 2x - 3

Now we need to form an equation for the area of the rectangle and solve it:

x(2x - 3) = 104

2x² - 3x = 104

2x² - 3x - 104 = 0 - now we need to factorize the equation

(2x + 13)(x - 8) = 0

Now we can say that x = 8 or x = -6.

Because we cannot have a negative length, x = 8 m.

Now we can workout the length using the expression that we formed at the beginning:

2x - 3 = l

2(8) - 3 = l

l = 16 - 3

l = 13 m

Answer 2

x-width
2x-3-length

A=lxw
104=(2x-3)(x)
104=2x^2-3x
52=x^2-3/2(x)
52+9/16=x^2-3/2(x)+9/16
841/16=(x-3/4)^2
29/4=x-3/4
x=32/4 or 8

length is 2(8)-3 which is 13 and width is 8