Question

7 (a) trouve les dimensions dun champ rectangulaire dont le périmètre est égal à 96 m et dont la longueur est égale à trois fois la largeur.

Explanation:

Step1: Define variables

Let the width of the rectangular field be \( w \) meters. Then the length \( l \) is \( 3w \) meters (since length is three times the width).

Step2: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know the perimeter \( P = 96 \) meters. Substitute \( l = 3w \) and \( P = 96 \) into the formula:
\[
96 = 2(3w + w)
\]

Step3: Simplify and solve for \( w \)

First, simplify the expression inside the parentheses:
\[
96 = 2(4w)
\]
\[
96 = 8w
\]
Now, solve for \( w \) by dividing both sides by 8:
\[
w=\frac{96}{8}=12
\]

Step4: Find the length

Since \( l = 3w \), substitute \( w = 12 \):
\[
l = 3\times12 = 36
\]

Answer:

The width of the rectangular field is \( 12 \) meters and the length is \( 36 \) meters.