Garden

The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m². Calculate the dimensions of the garden.

Correct answer:

a =  48.5 m
b =  16.5 m

Step-by-step explanation:

$$\begin{gathered} 2a+2b=130 \\ ab=800.25 \\ a(130-2a)\mathrm{/}2=800.25 \\ a(65-a)=800.25 \\ {a}^2-65a+800.25=0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{65\pm \sqrt{1024}}{2}} \\ {a}_{1,2}={\displaystyle \frac{65\pm 32}{2}} \\ {a}_{1,2}=32.5\pm 16 \\ {a}_1=48.5 \\ {a}_2=16.5 \\ a=48.5\text{ m} \end{gathered}$$

$b=16.5\text{ m}$

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