Here is a right-angled triangle - Edexcel - GCSE Maths - Question 2 - 2022 - Paper 3

To find the length of the missing side in a right-angled triangle, we can use the Pythagorean theorem, which states that:

$a^2 + b^2 = c^2$

where:

• $a$ and $b$ are the lengths of the legs of the triangle,
• $c$ is the length of the hypotenuse.

In this case, the lengths are:

• $a = 4 cm$ (one leg)
• $c = 8.5 cm$ (the hypotenuse)
• $b = x cm$ (the unknown leg)

Substituting the known values into the equation gives us:

$4^2 + x^2 = 8.5^2$

Calculating the squares:

$16 + x^2 = 72.25$

Next, we isolate $x^2$:

$x^2 = 72.25 - 16$ $x^2 = 56.25$

Now, we take the square root of both sides to find $x$:

$x = \\sqrt{56.25} = 7.5$

Thus, the value of $x$ is:

$x = 7.5 cm$