Question

3.

a. The total area of the model is 110 m2. Write an equation to find x. b. Solve the equation by completing the square.

A. (x + 2)(2x + 2) = 110; x = 5.93 m
B. (x + 2)(2x + 2) = 110; x = 3.53 m
C. (x + 2)(x + 2) = 110; x = 1.32 m
D. (x2 + 2)(2x + 2) = 110x; x = 5.93 m

Answer 1

A)

Explanation:

length = x +x + 2 = 2x + 2

Width = 2+ x

Area of rectangle = length *width

(x +2)(2x + 2) = 110

Use FOIL method

x*2x + x*2 + 2*2x + 2*2 = 110

2x² + 2x + 4x + 4 - 110 = 0 {Combine like terms}

2x² +6x - 106 = 0

a = 2 ; b = 6 ; c = -106

b² - 4ac = 6² - 4*2*(-106)

= 36 + 848

= 884

`\sqrt{b^(2)-4ac}=√(884)= 29.73`

`x =\frac{-b+\sqrt{b^(2)-4ac}}{2a} \ ; \ x==\frac{-b-\sqrt{b^(2)-4ac}}{2a}\\\\x = (-6+29.73)/(2*2) \ ; \ x =(-6-29.73)/(2*2) \ this \ is \ ignored \ as \ it \ is \ negative\\\\x=(23.73)/(4);`

x = 5.93 m