This diagram is mathematically incorrect as the unshaded triangle is supposed be right angled as well, but its dimensions don't satisfy the Pythagoras' theorem since 15² + 12² = 369 ≠ 20²

still make use of info that angle ADC is right angle

To be fair to a P5 student, the value of angle BDC and ADC aren't even given. Amd neither are stated as right angles.

Hence my earlier comment that it has to be assumed that BDC is right angled (which then would imply that ADC is right angled since AB is taken to be a straight line), since they're not expected to infer that the shaded triangle satisfies Pythagoras' Theorem and thus conclude BDC is 90°.

Or, assume that ADC is right angled.

How about use AD : BD = 3:1... are we able to find area for ABC... ?

Will still get 120 cm² for ABC

Meaning we still need to assume ADC is a right angle.Really mathematically error question;(

Yup. The teacher/set probably expects assumption to be done. Otherwise it could be that they forgot to mark either as a right angle.

If we let AC = AB be x instead,

Then x² = 12² + (x - 5)²

x² = 144 + x² - 10x + 25

10x = 169
x = 16.9

So what the teacher/setter should have done is let AB = AC = 16.9 cm