Answer:
i. [tex]x^{2}[/tex] + 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 = [tex]x^{2}[/tex] + 26x + 144
[tex]x^{2}[/tex] + 26x + 144 - 299 = 0
[tex]x^{2}[/tex] + 26x - 155 = 0
applying the trigonometric formula;
x = (-b ± [tex]\sqrt{b^{2} - 4ac}[/tex]) ÷ 2a
= (-26 ± [tex]\sqrt{(26)^{2} - 4(1*-155)}[/tex]) ÷ 2
= (-26 ± [tex]\sqrt{676 +620}[/tex]) ÷ 2
= (-26 ± [tex]\sqrt{1296}[/tex]) ÷ 2
= (-26 ± 36) ÷ 2
x = (-26 + 36) ÷ 2 OR x = (-26 -36) ÷ 2
= 10 ÷ 2 OR -62 ÷ 2
= 5 OR -31
Thus, x = 5
