# Rectangle - sides

What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?

Correct result:

x =  66 cm

#### Solution:

$ab = 266 \ \\ b = a + 5 \ \\ a(a+5) = 266 \ \\ a^2 + 5 a - 266 =0 \ \\ \ \\ a^2 +5a -266 =0 \ \\ \ \\ p=1; q=5; r=-266 \ \\ D = q^2 - 4pr = 5^2 - 4\cdot 1 \cdot (-266) = 1089 \ \\ D>0 \ \\ \ \\ a_{1,2} = \dfrac{ -q \pm \sqrt{ D } }{ 2p } = \dfrac{ -5 \pm \sqrt{ 1089 } }{ 2 } \ \\ a_{1,2} = \dfrac{ -5 \pm 33 }{ 2 } \ \\ a_{1,2} = -2.5 \pm 16.5 \ \\ a_{1} = 14 \ \\ a_{2} = -19 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (a -14) (a +19) = 0 \ \\ \ \\ \ \\ a = 14 \ \\ b= 19 \ \\ o = 2(a+b) = 66 \ \text{cm}$

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