Respuesta :
Answer:
Therefore,
Dimensions of the Original Square is
[tex]x =11\ m[/tex]
Step-by-step explanation:
Given:
Let the side of Square be "x" meter
Then the Dimensions of a Rectangle is formed by adding 6 m to one side and 3 m to the other side wil be.
[tex]Length = x+6\\\\Width=x+3[/tex]
Area of Rectangle =238 m²
To Find:
x = ? (Dimension of Original Square)
Solution:
Area of Rectangle is given by
[tex]\textrm{Area of Rectangle}=Length\times Width[/tex]
Substituting the values we get
[tex]238=(x+6)\times (x+3)[/tex]
Opening the Parenthesis we get
[tex]238=x^{2}+9x+18\\\\x^{2}+9x+-220=0[/tex] ......Which is Quadratic equation
On Factorizing and Splitting the middle term we get
[tex]x^{2}+20x-11x-220=0\\\\x(x+20)-11(x+20)=0\\\\(x+20)(x-11)=0\\\\x+20=0\ or\ x-11=0\\\\x=-20\ or\ x=11[/tex]
As distance cannot be negative therefore,
[tex]x =11[/tex]
Therefore,
Dimensions of the Original Square is
[tex]x =11\ m[/tex]
Answer:
11 meter
Step-by-step explanation:
Given: A rectangle is formed from a square by adding 6 m to one side and 3 m to the other side.
The area of the rectangle is 238 m².
Now, finding the dimension of the original square.
Lets assume the side of square be "s".
∴ Width= [tex]s+6[/tex]
Length= [tex]s+3[/tex]
We know, area of rectangle= [tex]width\times length[/tex]
Subtituting the value in the formula to find the dimension or side of square.
⇒
using distributive property of multiplication.
⇒[tex]238= s^{2} + 3s+6s+18[/tex]
Subtracting both side by 238
⇒ [tex]s^{2} + 9s-220= 0[/tex]
Solving by using quadratic formula to find value of s.
Formula: [tex]\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}[/tex]
∴ In the expression [tex]s^{2} +9s-220[/tex], we have a= 1, b= 9 and c= -220.
Now, subtituting the value in the formula.
= [tex]\frac{-9\pm \sqrt{9^{2}-4(1\times-220) } }{2\times1}[/tex]
= [tex]\frac{-9\pm \sqrt{81-4(-220) } }{2}[/tex]
= [tex]\frac{-9\pm \sqrt{81+880 } }{2}[/tex]
= [tex]\frac{-9\pm 31 }{2}[/tex]
= [tex]\frac{-40}{2} or\ \frac{22}{2}[/tex]
= -20 or 11
Ignoring negative result as dimension cannot be negative.
∴ The dimension of square will be 11 meter.
