Question

4.

a. The total area of the model is 130 m2. Write an equation to find x. b. Solve the equation by completing the square.


A. (x + 2)(2x + 2) = 130; x = 5.12 m

B. (x + 2)(2x + 2) = 130; x = 6.70 m

C. (x + 2)(x + 2) = 130; x = 9.40 m

D. (x + 2)(2x + 2) = 130; x = 6.58 m

Answer 1

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

x=6.58m

Explanation:

The shape of the whole figure is a triangle. Hence the area of the whole figure is expressed as:

Area = Length * Width

Given

Length = 2 + x + x = 2+2x

Width = 2 + x

Area = 130m²

Substitute the resultng values into the formula;

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

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

Expand the bracket:

`2x^2+2x+4x+4=130\\2x^2+6x+4=130\\`

Divide through by 2

`x^2+3x+2=65\\x^2+3x=65-2\\x^2+3x = 63`

Complete the square by adding the square of the half of the coefficient of x to both sides:

`(x^2+3x+((3)/(2) )^2)=63+((3)/(2) )^2`

`(x+(3)/(2) )^2=63 + (9)/(4) \\(x+(3)/(2) )^2=(252+9)/(4) \\(x+(3)/(2) )^2=(261)/(4)\\(x+(3)/(2) )^2=65.25`

Take the square root of both sides

`\sqrt{(x+((3)/(2) ))^2} = √(65.25)\\x+(3)/(2)= 8.078\\x=8.078-1.5\\x=6.58m`

Hence the value of x is 6.58m