Rectangle - area, perimeter

The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.

Correct result:

a =  20 m
b =  15 m

Solution:

S=300 m2 p=70 m S=ab p=2(a+b)  300=ab 35=a+b  a(35−a)=300  −a2+35a−300=0 a2−35a+300=0  p=1;q=−35;r=300 D=q2−4pr=352−4⋅1⋅300=25 D>0  a1,2=−q±D2p=35±252 a1,2=35±52 a1,2=17.5±2.5 a1=20 a2=15   Factored form of the equation:  (a−20)(a−15)=0  a=a1=20=20 m

Our quadratic equation calculator calculates it.

b=a2 b=35−a=35−20=15 m

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