# A rectangular patio

A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.

Correct result:

c =  30 ft
d =  40 ft

#### Solution:

$a=20 \ \text{ft} \ \\ b=30 \ \text{ft} \ \\ \ \\ (a+x)*(b+x)=2*a*b \ \\ \ \\ (20+x) \cdot \ (30+x)=2 \cdot \ 20 \cdot \ 30 \ \\ x^2 +50x -600=0 \ \\ \ \\ a=1; b=50; c=-600 \ \\ D=b^2 - 4ac=50^2 - 4\cdot 1 \cdot (-600)=4900 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ -50 \pm \sqrt{ 4900 } }{ 2 } \ \\ x_{1,2}=\dfrac{ -50 \pm 70 }{ 2 } \ \\ x_{1,2}=-25 \pm 35 \ \\ x_{1}=10 \ \\ x_{2}=-60 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -10) (x +60)=0 \ \\ \ \\ c=a+x_{1}=20+10=30 \ \text{ft}$

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$d=b+x_{1}=30+10=40 \ \text{ft}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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