Maths-
General
Easy

Question

A rectangular park is 6𝑥 + 2 𝑓𝑡 long and 3𝑥 + 7 𝑓𝑡 wide. In the middle of the park is a square turtle pond that is 8 𝑓𝑡 wide. What expression represents the area of the park not occupied by the turtle pond?




hintHint:

  • Area of rectangle is given by product of length and breadth.
  • Area of rectangle = length × breadth.
  • Area of rectangle = l × b.

The correct answer is: Hence, expression that represent the area of the park not occupied by the turtle pond is 18x2 + 48x - 50.


    Answer:
    • Step by step explanation: 
      • Given:
    Length of park = 6x + 2 units.
    Width of outer rectangle = 3x + 7 units.

    • Step by step explanation: 
      • Given:
    Length of park = 6x + 2 units.
    Width of outer rectangle = 3x + 7 units.
    Side of pond = x units.
    • Find area of park.
    Area of rectangle = l × b,
    So,
    Area of park = (6x + 2) × (3x + 7)
    Area of park = 6x × (3x + 7) + 2 (3x + 7)
    Area of park = 18x2 + 42x + 6x + 14
    Area of park = 18x2 + 48x + 14
    • Step 2:
    • Find area of pond.
    Area of pond = (a)2
    So,
    Area of pond = (8)2
    Area of pond = 64
    • Step 3:
    • Find area of park not occupied by pond:
    Area of park not occupied by pond = area of park – area of pond
    Area of park not occupied by pond = (18x2 + 48x + 14) – (64)
    Area of park not occupied by pond = 18x2 + 48x + 14 – 64
    Area of park not occupied by pond = 18x2 + 48x – 50

    • Final Answer:

                             Hence, expression that represent the area of the park not occupied by the turtle pond is 18x2 + 48x - 50.

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