Notice that the rectangle ACEG is divided into 2 identical right angled triangles ACE and AGE by the diagonal line AE.

So area of△ACE = area of△AGE

Now,

① Area△ACE = area△ABX + area □ BCDX
area△XDE

② Area△AGE = area△AHX + area rectangle HXFG + area△XFE


③Realise that △ABX = △AHX since they are identical halves of the rectangle ABXH, divided by the diagonal line AX.

④And, △XDE = △XFE since they are identical halves of the rectangle XDEF, divided by the diagonal line XE.

Since the areas in ① and ② are the same, and from the result in ③ and ④,

We realise that :

area □ BCDX = area rectangle HXFG
= 36cm²

Since the square has area 36cm²,

Its side lengths = √36 cm = 6cm

(Or realise that 6cm x 6cm = 36cm. Remember that any square always has 4 equal sides)


So BC = 6cm since it's a side of the square.

AC = AB + BC
= 9cm + 6cm
= 15cm

Um J , I think u should answer him in the answer section and not in the comments