ABC right angled triangle

[umair]

ABC is a right angled triangle, AB= 4, BC= 5. Whats the area?


Poss answers= More info needed, 12, 6, 20, 10


Now, in such a scenario is it valid to say more info is needed as you are not sure which way they have labelled the triangle or is it just a straight forward question?

 

[lookagain]

ABC is a right angled triangle, AB= 4, BC= 5. Whats the area?


Poss answers= More info needed, 12, 6, 20, 10


Now, in such a scenario is it valid to say more info is needed as you are not sure which way they have
labelled the triangle or is it just a straight forward question?

The following diagram is a typical set-up for a right triangle. But in the problem,
the length of AB = 4, and the length of BC = 5, so we cannot use this figure, because
it's not consistent with that. (Side a is necessarily shorter than c, not longer than it.)
Eliminating this set-up of a right triangle reduces the number of cases to consider.

----------------------------------------------------------------------------------


Instead, suppose you start with/anchor side AB as a base of the right triangle.

The answer choice will hinge on whether there are just the following two cases,
combined with whether their areas are different or are the same:

Case 1) Let the right angle of the right triangle be angle A. This forces BC to be
the hypotenuse. Then side CA is a leg. You have the 3-4-5 Pythagorean Triple
there. Then you use (1/2)(leg)(leg) to get the area of the triangle.


Case 2) Let the right angle of the right triangle be angle B. This forces BC to be
the other leg (AB being the first leg). Then side CA is the hypotenuse. But you don't
need to use the Pythagorean Theorem and/or know some common Pythagorean
Triples, because you already have the lengths of the legs to find the area of this right
triangle and you do not need the length of the hypotenuse. As before in the first case,
work out the area using the lengths of the two legs.


For example, if the two areas between the two cases wind up being different,
then the correct answer choice would be "More info needed."

 

[pka]

ABC is a right angled triangle, AB= 4, BC= 5. Whats the area?
Poss answers= More info needed, 12, 6, 20, 10
Now, in such a scenario is it valid to say more info is needed as you are not sure which way they have labelled the triangle or is it just a straight forward question?

Only your textbook author and/or your instructor can give you a definitive answer.

However, I know of at least two axiomatic geometry texts that use the convention that in naming a right triangle the middle letter is the name of the right angle. If you follow that convention then yes B is the right angle. That means one of the given possible answers is correct.

 

[sumit saurav]

answer could be 6 as a common example of pytahgoras theorem
5(sqre)= 4(sqre) +3(sqre)
leading to 4 and 3 as perpendicular and base

 

[Marvin Kalngan]

ABC is a right angled triangle, AB= 4, BC= 5. Whats the area?


Poss answers= More info needed, 12, 6, 20, 10


Now, in such a scenario is it valid to say more info is needed as you are not sure which way they have labelled the triangle or is it just a straight forward question?

a labeled figure is needed
area = 0.5*base*height
area = 0.5*5*4
area = 10 square units

or

area = 0.5*base*height
area = 0.5*4*5
area = 10 square units