Question

A. the total area of the model is 130 m2. write an equation to find x.

b. solve the equation by completing the square. (x + 2)(2x + 2) = 130; x = 5.12 m (x + 2)(2x + 2) = 130; x = 6.70 m (x + 2)(2x + 2) = 130; x = 6.58 m (x + 2)(x + 2) = 130; x = 9.40 m

Answer 1

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

`\rightarrow (x+(3)/(2))^2-[(3)/(2)]^2-63=0\\\\ (x+(3)/(2))^2=63 +(9)/(4)\\\\(x+(3)/(2))^2=(261)/(4)\\\\(x+(3)/(2))=\pm \sqrt{(261)/(4)}\\\\(x+(3)/(2))=\pm(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`

Option C:→ (x + 2)(2 x + 2) = 130; x = 6.58 m

Answer 2

the complete question in the attached figure

we know that

[area of rectangle]=b*h
b=(x+2)
h=(2x+2)
Area=130 m²

then

130=(x+2)*(2x+2)--------> 2x²+2x+4x+4-130=0--------> 2x²+6x-126=0

the answer Part a)
the equation to find x is
[2x²+6x-126=0]

b.) solve the equation by completing the square

130=(x+2)*(2x+2)

using a graph tool
see the attached figure

the solution is
x=6.58 m

the answer Part b) is
(x + 2)(2x + 2) = 130; x = 6.58 m