aling nena cuts a rectangular cloth with a perimeter of 150 meters. Write the function which represents the width(y) of the cloth as a function of the length(x)
a.y=150x
b.y=x150
c.y=150x+1
d.y=75-x
Answers
Answer:
Given:
\textsf{Perimeter of the rectangular room is 150m}Perimeter of the rectangular room is 150m
\underline{\textsf{To find:}}
To find:
\textsf{The relation connecting area and width}The relation connecting area and width
\underline{\textsf{Solution:}}
Solution:
\textsf{Let l and w be the length and width of the rectangle}Let l and w be the length and width of the rectangle
\textsf{Perimeter of the rectangular room=150 m}Perimeter of the rectangular room=150 m
\implies\mathsf{2(l+w)=150}⟹2(l+w)=150
\implies\mathsf{l+w=75}⟹l+w=75
\implies\mathsf{l=75-w}⟹l=75−w
\textsf{Area of the rectangular room}Area of the rectangular room
\mathsf{=}\,\textsf{Length}\mathsf{\times}\textsf{Breadth}=Length×Breadth
\mathsf{=l{\times}w}=l×w
\mathsf{=(75-w){\times}w}=(75−w)×w
\mathsf{=75w-w^2}=75w−w
2
\implies\mathsf{A(w)=75w-w^2}⟹A(w)=75w−w
2
y = 75 - x is the function represents the width(y) of the cloth as a function of the length(x) for rectangle of perimeter 150.
Given : A rectangular cloth with a perimeter of 150 meters is cut
To Find : the function which represents the width(y) of the cloth as a function of the length(x)
Solution:
Perimeter of a rectangle = 2 ( Length + width )
Length = x
Width = y
Perimeter = 150
=> 2 ( x + y) = 150
Dividing both sides by 2
=> x + y = 75
=> y = 75 - x
the function which represents the width(y) of the cloth as a function of the length(x) is y = 75 - x
Correct option is d) y = 75 - x
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