Answer:
l = 14 2/3
w = 9 1/3
Step-by-step explanation:
Let l = length
w = 2+ 1/2l
We know the perimeter is 48 and is given by
P = 2(l+w)
48 = 2(l + 2 +1/2l)
Distribute
48 = 2l+4+l
Combine like terms
48 = 3l +4
Subtract 4 from each side
48-4 = 3l+4-4
44= 3l
Divide each side by 3
44/3 = 3l/3
44/3 =l
14 2/3 =l
Now we need to find w
w = 2 + 1/2 l
=2 + 1/2(44/3)
= 2 +44/6
=12/6 +44/6
=56/6
=9 1/3
The Length of the rectangle is 14[tex]\frac{2}{3}[/tex] m and width 9[tex]\frac{1}{3}[/tex] m.
Step-by-step explanation:
Given,
Perimeter of the rectangle = 48 m
The width of the rectangle is 2 more than half the length.
To find the length and width of the rectangle.
Formula
Perimeter of the rectangle of length l and width b is = 2(l+b)
Let,
Length = l
Width = [tex]\frac{l}{2} +2[/tex] [ given]
Now,
According to the problem
2(l+[tex]\frac{l}{2} +2[/tex] ) = 48
or, [tex]l+\frac{l}{2} +2[/tex] = 24
or, [tex]\frac{3l}{2}[/tex] = 24-2
or, [tex]\frac{3l}{2}[/tex] = 22
or, l = [tex]\frac{22X2}{3}[/tex] = [tex]\frac{44}{3}[/tex] = 14[tex]\frac{2}{3}[/tex]
And width = [tex]\frac{44}{3X2}+2[/tex] = [tex]\frac{28}{3}[/tex] = 9[tex]\frac{1}{3}[/tex]
Hence,
Length = 14[tex]\frac{2}{3}[/tex] m and width = 9[tex]\frac{1}{3}[/tex] m
