Question

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1. mr. young is replacing the fencing around his rabbit pens and garden. the table shows the dimensions of the different areas. how many feet of fencing will he need to replace two rabbit pens and his garden? the perimeter of a rectangle is 2ℓ + 2w, where ℓ is the length and w is the width.

item	length (ft)	width (ft)
garden	12	10

Explanation:

Step1: Calculate perimeter of one rabbit pen

Using the formula for the perimeter of a rectangle \( P = 2\ell + 2w \), where \( \ell = 3.5 \) ft and \( w = 4.5 \) ft.
\( P_{\text{rabbit pen}} = 2\times3.5 + 2\times4.5 = 7 + 9 = 16 \) ft.

Step2: Calculate perimeter of two rabbit pens

Multiply the perimeter of one rabbit pen by 2.
\( P_{\text{two rabbit pens}} = 2\times16 = 32 \) ft.

Step3: Calculate perimeter of the garden

Using the same perimeter formula, with \( \ell = 12 \) ft and \( w = 10 \) ft.
\( P_{\text{garden}} = 2\times12 + 2\times10 = 24 + 20 = 44 \) ft.

Step4: Calculate total fencing needed

Add the perimeter of two rabbit pens and the perimeter of the garden.
\( \text{Total fencing} = 32 + 44 = 76 \) ft.

Answer:

76