Math, asked by hhussein95, 1 year ago

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).

B) write an expression for its length

C) what is the width of the rectangle she must make if Sheila want a rectangle that encloses the maximum area?

D) what is the area of the largest rectangle that Sheila can enclose with 100 inches of yam?

Answers

Answered by josimagic
0

Answer

It is given that, Sheila wants to enclose a rectangle with 100 inches of yarn.

So the perimeter of rectangle is 100/2 = 50

Therefore Length + width = 50

Let 'w' be the width of rectangle.

Width = w

Length = 50 - w

A) Write an expression for the area A of the rectangle in terms of w (width).

Area, A = length x width

        A = w(50 - w) = 50w - w^{2}

B) write an expression for its length

  Length = 50 - w

C) The width of the rectangle  that encloses the maximum area

    Sum of length and width is 50

      The product of length and width become maximum when

      length  50/2 +1 = 26 inches  and  

       width 50/2 -1 = 24 inches

D) The area of the largest rectangle that Sheila can enclose with 100 inches of yam

      Area = length x width = 26 x 24 = 624

      Area = 624 square inches

Answered by payalchatterje
0

Answer:

It is given that, Sheila wants to enclose a rectangle with 100 inches of yarn.

So the perimeter of rectangle is 100/2 = 50

Therefore Length + width=50

Let 'w' be the width of rectangle.

Width = w

Length = 50-w

A) Write an expression for the area A of the rectangle in terms of w (width).

Area, A = length x width

A = w(50-w) = 50w - w²

B) write an expression for its length

Length= 50-w

C) The width of the rectangle that encloses the maximum area

Sum of length and width is 50

The product of length and width become maximum when

length 50/2 +1 26 inches and

width 50/2 -1 = 24 inches

D) The area of the largest rectangle that Sheila can enclose with 100 inches of yam

Area = length x width = 26 x 24 = 624

Area = 624 square inches

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