Rectangle

The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.

Correct result:

a =  32.0377 cm
b =  5.4623 cm

Solution:

$$\begin{gathered} o=75\text{ cm } \\ u=32.5\text{ cm } \\ 2a+2b=o \\ {a}^2+b^2=u^2 \\ {a}^2+(o\mathrm{/}2-a{)}^2=u^2 \\ {a}^2+(75\mathrm{/}2-a{)}^2=32.5^2 \\ 2a^2-75a+350=0 \\ p=2;q=-75;r=350 \\ D=q^2-4pr=75^2-4\cdot 2\cdot 350=2825 \\ D>0 \\ {a}_{1,2}={\displaystyle \frac{-q\pm \sqrt{D}}{2p}}={\displaystyle \frac{75\pm \sqrt{2825}}{4}}={\displaystyle \frac{75\pm 5\sqrt{113}}{4}} \\ {a}_{1,2}=18.75\pm 13.2876822659 \\ {a}_1=32.0376822659 \\ {a}_2=5.46231773408 \\ \text{ Factored form of the equation: } \\ 2(a-32.0376822659)(a-5.46231773408)=0 \\ a=a_1=32.0377=32.0377\text{ cm} \end{gathered}$$

Our quadratic equation calculator calculates it.

$b=a_2=5.4623=5.4623\text{ cm}$

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