The area of triangle ABC is $oldsymbol{rac{ ext{√2}}{2}}$ m² - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 3

Since the area is given as $ext{√2}$ m², we can establish the equation:

rac{1}{2} imes (2x - 1) imes (x + 3) imes rac{ ext{√2}}{2} = ext{√2}

Multiplying both sides by $4$ to clear the fraction, we get:

$(2x - 1)(x + 3) = 4$

Expanding the left side gives:

$2x^2 + 6x - x - 3 = 4$

Which simplifies to:

$2x^2 + 5x - 7 = 0$

Now, we can solve for $x$ using the quadratic formula:

x = rac{-b ext{±} ext{√}(b^2 - 4ac)}{2a}

In our case, $a = 2$, $b = 5$, and $c = -7$. Plugging in these values, we get:

x = rac{-5 ext{±} ext{√}(5^2 - 4(2)(-7))}{2(2)}

Simplifying further:

x = rac{-5 ext{±} ext{√}(25 + 56)}{4}

x = rac{-5 ext{±} ext{√}(81)}{4}

x = rac{-5 ext{±} 9}{4}

Calculating the two possible values for $x$, we have:

1. x = rac{4}{4} = 1
2. x = rac{-14}{4} = -3.5

Since $x$ must be a positive length, we take:

$x = 1$

Thus, the final answer to 3 significant figures is:

1.00