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

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

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

In this triangle:

• The two shorter sides are 5.25 cm (the height) and x cm (the base).
• The longest side (the hypotenuse) is 18.75 cm.

Substituting the known values into the equation gives:

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

Calculating the squares:

• $(5.25)^2 = 27.5625$
• $(18.75)^2 = 351.5625$

Now the equation becomes:

$27.5625 + x^2 = 351.5625$

Subtract 27.5625 from both sides:

$x^2 = 351.5625 - 27.5625$

Thus, we find:

$x^2 = 324$

Taking the square root of both sides gives:

oot{2}{324} = 18$$ Finally, the value of x is: **x = 18 cm**.