Answer:
Length = 140 inches.
Step-by-step explanation:
Given : The length of a rectangle is two-fifths of its perimeter. if the width of the rectangle is 35 inches.
To find : what is its length in inches.
Solution : We have given
Length of rectangle = L.
Perimeter = P.
According to question
Length of a rectangle is two-fifths of its perimeter.
L = [tex]\frac{2}{5} * perimeter[/tex].
L= [tex]\frac{2}{5} * perimeter[/tex].
Width = 35 inches .
Perimeter = 2 ( length + breadth ) .
Plug the values of length = [tex]\frac{2}{5} * perimeter[/tex] ; Width = 35 inches .
Perimeter = 2 ( [tex]\frac{2}{5} * perimeter[/tex] + 35).
P = [tex]\frac{4}{5} * P + 70[/tex] .
On subtracting from both side by [tex]\frac{4}{5} * P[/tex] .
P - [tex]\frac{4}{5} * P[/tex] = 70 .
[tex]\frac{5 P - 4P}{5} [/tex] = 70 .
[tex]\frac{P}{5}[/tex] = 70.
On multiplying both side by 5
P = 70 *5
P = 350 inches .
Now , Plug value of perimeter in Length.
Length = [tex]\frac{2}{5}* perimeter[/tex].
Length = [tex]\frac{2}{5}* 350[/tex].
Length = 140 inches.
Therefore, Length = 140 inches.
