Question

The total area of the figure to the right is 299 cm². Use this fact to write an equation involving x. Then solve the

Answer 1

Answer:

i. $x^{2}$ + 26x + 144 - 299 = 0

ii. x = 5

Step-by-step explanation:

The area of the figure = 299 cm²

The figure has a shape of a rectangle, so that;

Area of rectangle = length x width

length of the figure = 18 + x

width of the figure = 8 + x

Area of the figure = (18 + x) x (8 + x)

299 = (18 + x) x (8 + x)

299 = $x^{2}$ + 26x + 144

$x^{2}$ + 26x + 144 - 299 = 0

$x^{2}$ + 26x - 155 = 0

applying the trigonometric formula;

x = (-b ± $\sqrt{b^{2} - 4ac}$) ÷ 2a

= (-26 ± $\sqrt{(26)^{2} - 4(1*-155)}$) ÷ 2

= (-26 ± $\sqrt{676 +620}$) ÷ 2

= (-26 ± $\sqrt{1296}$) ÷ 2

= (-26 ± 36) ÷ 2

x = (-26 + 36) ÷ 2  OR x = (-26 -36) ÷ 2

  = 10 ÷ 2 OR -62 ÷ 2

  = 5 OR -31

Thus, x = 5