Rectangle field

The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?

Correct result:

x =  102 m
y =  114 m

Solution:

119 19=(119x) (19+y) 2(119+19)+24=2 ((119x)+(19+y))  y=x+12  11919=(119x)(19+(x+12))  119 19=(119x) (19+(x+12)) x288x1428=0  a=1;b=88;c=1428 D=b24ac=88241(1428)=13456 D>0  x1,2=b±D2a=88±134562 x1,2=88±1162 x1,2=44±58 x1=102 x2=14   Factored form of the equation:  (x102)(x+14)=0  x=x1=102 m119 \cdot \ 19=(119-x) \cdot \ (19+y) \ \\ 2(119+19) + 24=2 \cdot \ ((119-x)+(19+y)) \ \\ \ \\ y=x+12 \ \\ \ \\ 119*19=(119-x)*(19+(x+12)) \ \\ \ \\ 119 \cdot \ 19=(119-x) \cdot \ (19+(x+12)) \ \\ x^2 -88x -1428=0 \ \\ \ \\ a=1; b=-88; c=-1428 \ \\ D=b^2 - 4ac=88^2 - 4\cdot 1 \cdot (-1428)=13456 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 88 \pm \sqrt{ 13456 } }{ 2 } \ \\ x_{1,2}=\dfrac{ 88 \pm 116 }{ 2 } \ \\ x_{1,2}=44 \pm 58 \ \\ x_{1}=102 \ \\ x_{2}=-14 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -102) (x +14)=0 \ \\ \ \\ x=x_{1}=102 \ \text{m}

Checkout calculation with our calculator of quadratic equations.

y=x+12=102+12=114 a=119x=119102=17 m b=19+y=19+114=133 m  y=114 my=x+12=102+12=114 \ \\ a=119-x=119-102=17 \ \text{m} \ \\ b=19+y=19+114=133 \ \text{m} \ \\ \ \\ y=114 \ \text{m}



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