Question

A walkway surrounds a rectangular garden. The width of the garden is 8 feet, and the length is 6 feet. The width x of the walkway around the garden is the same on every side. Write an expression that represents the total area of the garden and walkway.
- Draw a picture

Answer 1

Given :-

• AB = 8 feet .
• BC = 6 feet .
• ABCD is a garden .

To Find :-

• Total Area of garden ?
• Total Area of walkway ?

Solution :-

we know that,

• Area of rectangle = Length * Breadth .

so,

→ Area of garden = 8 * 6 = 48 feet². (Ans.)

now,

→ Length of Rectangle EFGH = (8 + 2x) feet .

→ Length of Rectangle EFGH = (6 + 2x) feet .

then,

→ Area of Rectangle EFGH = (8 + 2x) * (6 + 2x) = 48 + 16x + 12x + 4x² = (4x² + 28x + 48) feet².

therefore,

→ Total Area of walkway = Area of Rectangle EFGH - Area of garden = (4x² + 28x + 48) - 48 = 4x² + 28x + 48 - 48 = 4x² + 28x = 4(x² + 7x) feet². (Ans.)

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