Question

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.

Answer 1

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.