The length and width of the rectangle is 10 m and 4.5 m respectively.
Step-by-step explanation:
Given,
The length of a rectangle is 1 m more than twice the width.
Area of the rectangle = 45 sq m
To find the length and width of the rectangle.
Formula
If the length and width of a rectangle be l and b respectively, the area will be lb.
Let, the width (b) be = x and
Length (l) = 2x+1
According to the problem,
(2x+1)x = 45
or, [tex]2x^{2} +x = 45[/tex]
or, [tex]2x^{2}+x-45 = 0[/tex]
or, [tex]2x^{2}+(10-9)x-45 = 0[/tex]
or, [tex]2x^{2}+10x-9x-45 = 0[/tex]
or, 2x(x+5)-9(x+5) = 0
or, (2x-9)(x+5) =
Hence,
2x-9 = 0 and x+5 = 0
or, x = [tex]\frac{9}{2}[/tex] and x= -5
We will take x = [tex]\frac{9}{2}[/tex] as the value of length cannot be negative.
So,
Width = 4.5 m and Length = 2×4.5+1 = 10 m
