Question

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).

Answer 1

let the length of rectangle be L
let the breadth of rectangle be B

area of rectangle = L X B --------------------- (1)

PERIMETER OF RECTANGLE = 2(L+B) = 100

2L + 2B = 100
L+B =50

L=50-B------------------- (2)


SUBSTITUTE 2 IN 1

A= (50-B) X B

A = 50B - B²

Answer 2

Let the  length of the rectangle = l
 Let the  width of the rectangle = w
we know that ,
area  of the rectangle =Length×Breadth
A = l × w............(1) [from above]
According to the question,
2l + 2w = 100 
⇒2( l + w) = 100
⇒ (l+w) = 50
⇒ l = 50 - w...........(2) [From above]
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