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I totally missed the part about A, B, C, and D each being a distinct point on a plane. I was like, "how do we know that angle B is 90 degrees?" then when I finally saw the word "distinct," everything clicked.

Cant dis problem b solved by 30-60-90 theorem (as we know the point A B C D are distinct points, so AB is not equal to BC) thus making stmnt 1 sufficient to find the value of BC and hence the value of AB*BC.

Why should the triangle be 30-60-90 one? Not all right triangle have 30-60-90 angles.
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I think this the explanation isn't clear enough, please elaborate. When the 2nd statement says "The product of the non-hypotenuse sides of triangle ABC is equal to 24", can it not mean that the product of BD*AC =24 or BD*CB = 24. As BD is part of the triangle ABC. I think I overthought this question!

I think this the explanation isn't clear enough, please elaborate. When the 2nd statement says "The product of the non-hypotenuse sides of triangle ABC is equal to 24", can it not mean that the product of BD*AC =24 or BD*CB = 24. As BD is part of the triangle ABC. I think I overthought this question!

Non-hypotenuse sides of triangle ABC are AB and BC.
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In the second statement, it says the product of 2 non hypotenuse sides is 24. Then in that case, it can have multiple answers such as 2*12, 3*8, 4*6. With help of statement 1, we can say that AB*AC is 6*4 only. Hence, my doubt is, why cant the answer be C ?

In the second statement, it says the product of 2 non hypotenuse sides is 24. Then in that case, it can have multiple answers such as 2*12, 3*8, 4*6. With help of statement 1, we can say that AB*AC is 6*4 only. Hence, my doubt is, why cant the answer be C ?

The question asks to find the value of AB*BC. (2) says that AB*BC = 24. We have our answer! Does it matter whether it's 1*24, 1/2*48, 500*24/500, or anything else?
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Statement 2 says that the product of non hypotenuse sides is 24. Why are we not considering BD here?

Can among AB, BC or BD, any of the two sides be non hypotenuse side ?

Happy new Year.

Regards

(2) says: The product of the non-hypotenuse sides of triangle ABC is equal to 24. In triangle ABC, AC is hypotenuse, so non-hypotenuse sides are AB and BC. I think this is shown/explained on previous two pages several times.
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Statement 2 says that the product of non hypotenuse sides is 24. Why are we not considering BD here?

Can among AB, BC or BD, any of the two sides be non hypotenuse side ?

Happy new Year.

Regards

(2) says: The product of the non-hypotenuse sides of triangle ABC is equal to 24. In triangle ABC, AC is hypotenuse, so non-hypotenuse sides are AB and BC. I think this is shown/explained on previous two pages several times.

Thank you for your prompt reply. Sorry! I might have missed to check thoroughly.
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I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi, in this right angled triangle we can take AB or BC as the height ? why are we taking another height BD? im also not clear how we know that B must be the right angle if BD is the height?kindly explain im really confused. Thanks a lot in advance.

I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Hi, in this right angled triangle we can take AB or BC as the height ? why are we taking another height BD? im also not clear how we know that B must be the right angle if BD is the height?kindly explain im really confused. Thanks a lot in advance.

I think all your doubts are already answered in this topic. Please read the whole discussion.