Find answers, ask questions, and connect with our
community around the world.

Activity Discussion Math CLASS 7TH PERIMETER AND AREA

  • CLASS 7TH PERIMETER AND AREA

    Posted by Prateek on June 17, 2023 at 4:33 pm

    A wire is bent in the form of a rectangle having length twice the breadth. The same wire is bent in the form of a circle. It was found that the area of the circle is greater than that of the rectangle by 104.5cm2. Find the length of the wire.

    Majida replied 1 year, 1 month ago 2 Members · 1 Reply
  • 1 Reply
  • Majida

    Member
    June 18, 2023 at 11:30 am
    Helpful
    Up
    0
    Down
    Not Helpful
    ::

    Let the breadth of the rectangle be “b”.

    The length of the rectangle is twice the breadth, so it’s “2b”.

    The perimeter of the rectangle is 2x(b+2b) =6b.

    The wire bent in the form of a circle also has a circumference of 6b.

    Let “r” be the radius of the circle, that is,

    2πr=6b, implies, r= 6b/2π

    The area of the rectangle is 2b², and the area of the circle is 9b².

    So, according to the question, we have,

    Area of the circle – Area of the rectangle = 104.5

    9b² – 2b² = 104.5

    7b² = 104.5

    b² = 104.5 / 7

    b² = 14.93

    b ≈ √14.93 = 3.86

    The total length of the wire used is equal to the perimeter of the rectangle:

    Total length of wire = 6b
    = 6 × 3.86
    = 23.16

    Therefore, the length of the wire is approximately 23.16 cm.

For Worksheets & PrintablesJoin Now
+