Yeah
Thank you for your explanations

How do u get 13 x 13 ?

Length of inner square

= 12cm - 5cm = 7cm

Area of inner square
= 7cm × 7cm
= 49cm²


Area of 4 triangles

= 4 × ½ × base × height
= 2 × 5cm × 12cm
= 120cm²

Area of big square

= Area of the triangles and inmer square combined

= 120cm² + 49cm²
= 169cm²

How to get 13?

Because, the area of square = length × length

You need the same value multiplied by itself.


So in order to get 169 for the square area, we can do our times table and work our way up until we get 169.


1 × 1 = 1
2 × 2 = 4
3 × 3 = 9
..
..
12 × 12 = 144
13 × 13 = 169


(You should be familiar with times table up to 12 × 12 by now i.e know it by heart)


Given that 12 × 12 = 144, we can already start from here instead of lower numbers, since 144 is closer to 169.

So the side AB has to be 13

Oh so just find the side lenght of the big square then can the answer already. Thank for your clear explanation

Alternatively, this is a paper 2 question so calculator is allowed.


Use the square root function (√)


√169 = 13

Yes, because all the triangles are identical.

This length AB is the longest side of ABC. Since the triangles are all identical, then their longest side basically is the length AB.

This longest side corresponds to the length of the big square (notice how the triangles are placed. The longest side forms the sides of the square)


For such right-angled triangles, the longest side is called the hypotenuse. It is always directly opposite the right angle.

Alternatively, we could have used Pythagoras' Theorem (useful for Math Olympiad, but probably not allowed at P5)

For a right angled triangle with sides a,b and c, where c is the longest,


a² + b² = c²

(Note that a² means a × a)

So for this triangle,

5² + 12² = c²
25 + 144 = c²
169 = c²
c = √169 = 13