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A rectangle has a length of √ 72 meters and a width of √ 18 meters. Find its perimeter in exact and approximate forms, and then find its area.

The exact perimeter is _________ meters.

This is approximately ___________ meters. (Round your answer to the nearest tenth)

The area of the rectangle is ____________ square meters.

User FuzzyTew
by
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1 Answer

1 vote

Answer:

The exact perimeter is
18√(2) meters.

This is approximately 25.5 meters (nearest tenth).

The area of the rectangle is 36 square meters.

Explanation:

Area of a rectangle = width × length

Perimeter of a rectangle = (2 × width) + (2 × length)

Given:

  • length =
    √(72) m
  • width =
    √(18) m

Perimeter


\textsf{Perimeter}=2 √(18) +2√(72)


=2 √(9 \cdot 2) +2√(36 \cdot 2)


=2 √(9) √(2)+2√(36)√(2)


=2 \cdot 3 √(2)+2\cdot 6√(2)


=6 √(2)+12√(2)


=18√(2) \textsf{ m}

The exact perimeter is
18√(2) meters.

This is approximately 25.5 meters (nearest tenth).

Area


\textsf{Area}=√(18) * √(72)


=√(9 \cdot 2) * √(36 \cdot 2)


=3√(2) * 6√( 2)


=18√(2)√( 2)


=18 \cdot 2


=36 \textsf{ m}^2

The area of the rectangle is 36 square meters.

User Jacob Waller
by
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