Harold

Harold made a rectangular dog run in his backyard. The area of the dog run is 96 square feet. What are three different possible dimensions of dog run?

Correct answer:

a₁ =  8 ft
b₁ =  12 ft
a₂ =  6 ft
b₂ =  16 ft
a₃ =  4 ft
b₃ =  24 ft

Step-by-step explanation:

$$\begin{gathered} S=96{\text{ft}}^2 \\ S=a\cdot b \\ 0<a<b \\ a\cdot b=96=2^5\times 3 \\ {a}_1=8\text{ft} \\ {a}_2=6\text{ft} \\ {a}_3=4\text{ft} \\ {a}_4=3\text{ft} \\ {a}_5=2\text{ft} \\ {a}_6=1\text{ft} \end{gathered}$$

$b_1=S/a_1=96/8=12\text{ft}$

$b_2=S/a_2=96/6=16\text{ft}$

$b_3=S/a_3=96/4=24\text{ft}$

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