Diagonal of the rectangle

Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.

Correct result:

u =  10.8167

Solution:

S=54 o=30 S=a⋅ b o=2⋅ (a+b) S=a⋅ (o/2−a) 54=a∗(30/2−a)  54=a⋅ (30/2−a) a2−15a+54=0  p=1;q=−15;r=54 D=q2−4pr=152−4⋅1⋅54=9 D>0  a1,2=−q±D2p=15±92 a1,2=15±32 a1,2=7.5±1.5 a1=9 a2=6   Factored form of the equation:  (a−9)(a−6)=0 a=a1=9 b=a2=6 u=a2+b2=92+62=3 13=10.8167

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