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

equation to find the value of x.

The equation is
Enter your answer in the answer box and then click Check Answer

Answer 1

i.
`x^(2)` + 26x + 144 - 299 = 0

ii. x = 5

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 ±
`√(676 +620)`) ÷ 2

= (-26 ±
`√(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