Question

(b) la longueur d’un rectangle a 8 cm de plus que sa largeur. trouve les dimensions de ce rectangle sachant que le périmètre est de 64 cm.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( x \) cm. Then the length is \( x + 8 \) cm (since the length is 8 cm more than the width).

Step2: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). We know the perimeter is 64 cm, so we can set up the equation:
\[
2\times((x + 8) + x) = 64
\]

Step3: Simplify and solve the equation

First, simplify the left - hand side of the equation:
\[
2\times(2x + 8)=64
\]
Divide both sides of the equation by 2:
\[
2x + 8=\frac{64}{2}=32
\]
Subtract 8 from both sides:
\[
2x=32 - 8 = 24
\]
Divide both sides by 2:
\[
x=\frac{24}{2}=12
\]

Step4: Find the length

Since the length is \( x + 8 \), substitute \( x = 12 \) into this expression. The length is \( 12+8 = 20 \) cm.

Answer:

The width of the rectangle is 12 cm and the length is 20 cm.