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# 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?

Hint:

- 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 = 18x^{2} + 42x + 6x + 14

Area of park = 18x^{2} + 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 = (18x^{2} + 48x + 14) – (64)

Area of park not occupied by pond = 18x^{2} + 48x + 14 – 64

Area of park not occupied by pond = 18x^{2} + 48x – 50

- Final Answer:

Hence, expression that represent the area of the park not occupied by the turtle pond is 18x^{2} + 48x - 50.

- Given:

- Given:

^{2}+ 48x - 50.

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