Perimeter and diagonal

The perimeter of the rectangle is 82 m, the length of its diagonal is 29 m. Find the dimensions of the rectangle.

Correct result:

a =  21 m
b =  20 m

Solution:

o=82 m u=29 m  u2=a2+b2 o=2(a+b)  u2=a2+(o/2−a)2  292=a2+(82/2−a)2 −2a2+82a−840=0 2a2−82a+840=0  p=2;q=−82;r=840 D=q2−4pr=822−4⋅2⋅840=4 D>0  a1,2=−q±D2p=82±44 a1,2=82±24 a1,2=20.5±0.5 a1=21 a2=20   Factored form of the equation:  2(a−21)(a−20)=0 a=a1=21=21 m

Our quadratic equation calculator calculates it.

b=a2=20=20 m

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