Answer with explanation:
Length of the Model which is in the shape of rectangle= (x+2) meter
Breadth of the Model which is in the shape of rectangle = (2 x + 2) meter
Area of Rectangle = Breadth × Length
→(x+2)×(2 x +2)=130
→x×(2 x +2) +2×(2 x +2)=130
→2 x²+2 x +4 x +4=130→→Using Distributive property of Multiplication with respect to addition which is, a×(b+c)=a×b +a×c
→2 x²+ 6 x +4-130=0
→2 x²+ 6 x-126=0
→2×(x²+3 x -63)=0
→x²+3 x -63=0
→→Solution of Quadratic by completing the square
[tex]\rightarrow (x+\frac{3}{2})^2-[\frac{3}{2}]^2-63=0\\\\ (x+\frac{3}{2})^2=63 +\frac{9}{4}\\\\(x+\frac{3}{2})^2=\frac{261}{4}\\\\(x+\frac{3}{2})=\pm \sqrt{\frac{261}{4}}\\\\(x+\frac{3}{2})=\pm\frac{16.16}{2}\\\\x+1.50=8.08\\\\\text{as sides of rectangle can't be negative}}\\\\x=8.08 -1.50\\\\x=6.58[/tex]
Option C:→ (x + 2)(2 x + 2) = 130; x = 6.58 m
