Rectangle

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

Result

a =  32.038 cm
b =  5.462 cm

Solution:

2a+2b=75 a2+b2=32.52  a2+(75/2a)2=32.52 2a275a+350=0  p=2;q=75;r=350 D=q24pr=75242350=2825 D>0  a1,2=q±D2p=75±28254=75±51134 a1,2=18.75±13.287682265918 a1=32.037682265918 a2=5.4623177340817   Factored form of the equation:  2(a32.037682265918)(a5.4623177340817)=0 a=a1=32.037732.037732.038 cm2a+2b=75 \ \\ a^2+b^2=32.5^2 \ \\ \ \\ a^2+(75/2-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}=\dfrac{ -q \pm \sqrt{ D } }{ 2p }=\dfrac{ 75 \pm \sqrt{ 2825 } }{ 4 }=\dfrac{ 75 \pm 5 \sqrt{ 113 } }{ 4 } \ \\ a_{1,2}=18.75 \pm 13.287682265918 \ \\ a_{1}=32.037682265918 \ \\ a_{2}=5.4623177340817 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 2 (a -32.037682265918) (a -5.4623177340817)=0 \ \\ a=a_{1}=32.0377 \doteq 32.0377 \doteq 32.038 \ \text{cm}

Checkout calculation with our calculator of quadratic equations.

b=a2=5.46235.46235.462 cmb=a_{2}=5.4623 \doteq 5.4623 \doteq 5.462 \ \text{cm}



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