Respuesta :
Answer:
Length of the rectangle = 16 inches
Width of the rectangle = 12 inches
Step-by-step explanation:
Let the length of the rectangle be represented by x.
Then width can be expressed as [tex]\[\frac{x}{2}+4\] [/tex]
Perimeter of a rectangle is the sum of four sides of the rectangle.
This can be expressed as 2*(length + breadth)
= [tex]\[2* (x + \frac{x}{2}+4)\][/tex]
= [tex]\[2* (\frac{3x}{2}+4)\][/tex]
= [tex]\[3x + 8\][/tex]
But perimeter is given as 56.
So, [tex]\[3x + 8 = 56\] [/tex]
=> [tex]\[3x = 48\][/tex]
=> [tex]\[x = 16\][/tex]
Hence length of the rectangle = 16 inches
Width of the rectangle = [tex]\[\frac{16}{2}+4\][/tex] = 12 inches
Answer:
length = 16 inches and width = 12 inches
Step-by-step explanation:
Let l be the length and w be the width of the rectangle.
It is given that width is 4 inches greater than half of the length:
[tex]w=\frac{l}{2}+4[/tex] ------1
Perimeter of the rectangle is given by [tex]2\times(l+w)[/tex]
[tex]2\times(l+w)=56[/tex]
[tex]l+w=28[/tex] ----------------2
Substituting w from equation 1 in equation 2, we get:
[tex]l+(4+\frac{l}{2})=28[/tex]
[tex]\frac{3l}{2}=24[/tex]
∴ l = 16 inches
Putting l=16 in equation 1, we get w=12.
Hence w= 12 inches.
