Question

place what we know in the formula. p = 36 cm; p = (2 x 8) + 2l; 36 = 16 + 2l; 36 - 16 = 20; 20 = 2 lengths; divide 20 by 2 to get the length of one side; 20 ÷ 2 = 10 cm so each length is 10cm. 8 cm; 8 cm; p = l + l + w + w; p = (2 x width) + (2 x length)

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times\text{width}+ 2\times\text{length} \) (or \( P=\text{length}+\text{length}+\text{width}+\text{width} \)). We know the perimeter \( P = 36\space\text{cm} \) and the width \( w = 8\space\text{cm} \).

Step2: Substitute the known values into the formula

Substitute \( P = 36 \) and \( w = 8 \) into \( P=2\times w + 2\times l \) (where \( l \) is the length). So we get \( 36=(2\times8)+2l \).

Step3: Simplify the right - hand side of the equation

Calculate \( 2\times8 = 16 \), so the equation becomes \( 36 = 16+2l \).

Step4: Isolate the term with the length

Subtract 16 from both sides of the equation: \( 36 - 16=2l \). Since \( 36-16 = 20 \), we have \( 20 = 2l \).

Step5: Solve for the length

Divide both sides of the equation \( 20 = 2l \) by 2. Using the division operation \( l=\frac{20}{2} \), we find that \( l = 10\space\text{cm} \).

Answer:

The length of each side (the length of the rectangle) is 10 cm.