Question

the unity flag is one of the largest canadian flags. the length is twice the width and the area is $167.2\\ m^2$. find the dimensions of the unity flag, to the nearest tenth of a metre.

Explanation:

Step1: Define variables

Let the width of the flag be \( w \) meters. Then the length \( l \) is \( 2w \) meters (since length is twice the width).

Step2: Use area formula for rectangle

The area \( A \) of a rectangle is given by \( A = l \times w \). Substituting \( l = 2w \) and \( A = 167.2 \) into the formula, we get:
\[
167.2=(2w)\times w
\]
Simplify the right - hand side:
\[
167.2 = 2w^{2}
\]

Step3: Solve for \( w \)

First, divide both sides of the equation \( 2w^{2}=167.2 \) by 2:
\[
w^{2}=\frac{167.2}{2}=83.6
\]
Then, take the square root of both sides to find \( w \):
\[
w=\sqrt{83.6}\approx9.1
\]

Step4: Find the length

Since \( l = 2w \), substitute \( w\approx9.1 \) into the formula for \( l \):
\[
l = 2\times9.1 = 18.2
\]

Answer:

The width of the Unity Flag is approximately \( 9.1 \) meters and the length is approximately \( 18.2 \) meters.