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

Answer:

The exact perimeter is $18\sqrt{2}$ meters.

This is approximately 25.5 meters (nearest tenth).

The area of the rectangle is 36 square meters.

Step-by-step explanation:

Area of a rectangle = width × length

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

Given:

• length = $\sqrt{72}$ m
• width = $\sqrt{18}$ m

Perimeter

$\textsf{Perimeter}=2 \sqrt{18} +2\sqrt{72}$

               $=2 \sqrt{9 \cdot 2} +2\sqrt{36 \cdot 2}$

               $=2 \sqrt{9} \sqrt{2}+2\sqrt{36}\sqrt{2}$

               $=2 \cdot 3 \sqrt{2}+2\cdot 6\sqrt{2}$

               $=6 \sqrt{2}+12\sqrt{2}$

               $=18\sqrt{2} \textsf{ m}$

The exact perimeter is $18\sqrt{2}$ meters.

This is approximately 25.5 meters (nearest tenth).

Area

$\textsf{Area}=\sqrt{18} \times \sqrt{72}$

       $=\sqrt{9 \cdot 2} \times \sqrt{36 \cdot 2}$

       $=3\sqrt{2} \times 6\sqrt{ 2}$

       $=18\sqrt{2}\sqrt{ 2}$

       $=18 \cdot 2$

       $=36 \textsf{ m}^2$

The area of the rectangle is 36 square meters.