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i dont understand why the answer is C since we dont know which sides are equal

you dont need that actually. you have 2 sides measures - 9, 4 and you know that its an isosceles triangle. so possibility 1 - 3rd side is 9 or possibility 2 - 3rd side is 4.

now check... that if 3rd side is 4.. then triangle is 9,4, 4 as per the properties of any triangle sum of 2 sides is greater than 3rd side, here 4 + 4 is not gr than 9.. so this construction is not possible.

Well, I chose E, but I see your explanation and agree with C. However, the question mentions "isosceles RIGHT triangle", which means that one angle is 90 degrees. If the equal sides are both 9, then the hypotenuse must be longer. But with sides 9 9 4, it's obviously not a right triangle. So the word "right" must be removed from the question to have C as the correct answer.

Well, I chose E, but I see your explanation and agree with C. However, the question mentions "isosceles RIGHT triangle", which means that one angle is 90 degrees. If the equal sides are both 9, then the hypotenuse must be longer. But with sides 9 9 4, it's obviously not a right triangle. So the word "right" must be removed from the question to have C as the correct answer.

Either of the options is insufficient alone, however taking both together is disapproving question stem itself. However assuming that a typo, Option 'C' is the correct one.
_________________

What is the perimeter of the isoceles right triangle ABC

S1 AB = 9

S2 BC = 4

In case the triangle is right angled isosceles triangle the OA should be E. Because clearly S1 and S2 are not sufficient individually

So combining S1 and S2 we get 2 values i.e. Sides with 4,4,9 which is NOT possible and the second is 4,9,9 which is not right angled. If we would have had the knowledge which angle is right angled. Then it could be solved.

What is the perimeter of the isoceles right triangle ABC

S1 AB = 9

S2 BC = 4

In case the triangle is right angled isosceles triangle the OA should be E. Because clearly S1 and S2 are not sufficient individually

So combining S1 and S2 we get 2 values i.e. Sides with 4,4,9 which is NOT possible and the second is 4,9,9 which is not right angled. If we would have had the knowledge which angle is right angled. Then it could be solved.

In case the isosceles triangle is right-angled, the question would be WRONG. However, the question is correct and the answer is "C". Also, we can infer from the given statements that the triangle is not an isosceles right triangle.
_________________

What is the perimeter of the isoceles right triangle ABC

S1 AB = 9

S2 BC = 4

In case the triangle is right angled isosceles triangle the OA should be E. Because clearly S1 and S2 are not sufficient individually

So combining S1 and S2 we get 2 values i.e. Sides with 4,4,9 which is NOT possible and the second is 4,9,9 which is not right angled. If we would have had the knowledge which angle is right angled. Then it could be solved.

In case the isosceles triangle is right-angled, the question would be WRONG. However, the question is correct and the answer is "C". Also, we can infer from the given statements that the triangle is not an isosceles right triangle.

I don't think the question will be wrong if the triangle is right angled isosceles triangle. We can have a real number as the 3rd side. If one of the statement had mentioned that the triangle is right angled at B. then AC could be calculated and hence the perimeter

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