# As part of a collage for her art class, Sheila wants to enclose a rectangle with 100 inches of yarn. Write an expression for the area A of the rectangle in terms of w (width). Please show solutions Thank you

1
by Darkfury

2016-05-01T11:16:26+05:30

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A rectangle is a closed figure which has it's opposite sides equal.
let,
the length of the rectangle = l
width of the rectangle = w
we know that ,
area  of the rectangle (A)  = length (l) × breadth (w)
⇒ A = l × w............(1)
now, according to the question,
2l + 2w = 100 ( perimeter of the rectangle enclosed with 100 inch yarn)
⇒2( l + w) = 100
⇒ (l+w) = 50
⇒ l = 50 - w...........(2)
now , substitute (2) in (1).
⇒ A = (50 - w) × w
⇒ A = 50w - w²
Hence , area of the rectangle in terms of width (w) is
A = 50w - w²