How to solve 2nd hardest PSLE Math 2025 question easily

Question: Rectangle ABCD contains 2 identical squares inside it as shown. The ratio of AB to BD is 5 : 2. What’s BD?

First step is to let 1 side of the square be 1unit.

Next, create the equation
AB = 29 + 1u + 29 = 1u + 58cm
BD = 1u + 10cm

Since the ratio of

AB : BD is

5 : 2

and

1u + 58cm : 1u + 10cm

We cross multiply!

2 x (1u + 58cm) = 5 x (1u + 10cm)

2u + 116cm = 5u + 50cm

3u = 116 - 50 = 66cm

1u = 66 ÷ 3 = 22 cm

AB = 22 + 58 = 80cm!

Don't forget to double check

BD = 22 + 10 = 32cm

AB : BD

80 : 32

÷ 16 : ÷ 16 (Simplify)

5 : 2 (Which is correct!)