Here is a right-angled triangle - OCR - GCSE Maths - Question 18 - 2018 - Paper 1

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

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

where $c$ is the length of the hypotenuse, and $a$ and $b$ are the lengths of the other two sides.

In this triangle, we can identify:

• $a = 5.25 \text{ cm}$
• $c = 18.75 \text{ cm}$
• $b = x \text{ cm}$ (the side we're trying to find)

Plugging in the known values into the Pythagorean theorem gives:

$(5.25)^2 + x^2 = (18.75)^2$

Calculating the squares:

$27.5625 + x^2 = 351.5625$

Now, isolate $x^2$:

$x^2 = 351.5625 - 27.5625$ $x^2 = 324$

Taking the square root of both sides:

$x = \sqrt{324}$ $x = 18$

Thus, the value of x is:

$x = 18 \text{ cm}$