What is the area of the triangle ABC?

Question

(1) The triangle is inscribed in a semicircle with its diameter as one side of the triangle.The radius of the Semicircle is 10

(2) The triangle is an isosceles triangle.

summer101 · Answer

Statement 1:  Inscribed in a semicircle means the angle facing opposite the diameter is 90 degree. Area = 1/2*b*h. b =20. h or height we don't know. h will be different if the triangle is 90-45-45, or 90-30-60. Hence Insufficient
 Statement 2:  Says its isosceles, but no other detail. no angles, no base or height data. Hence Insufficient.

together we know the triangle is 90-45-45, with base 20. Hence area can be calculated. Sufficient. Ans is C

Vamshi8411 · Answer

The angle opposite to the Diameter(i.e., hypotenuse) is 90, so if we draw a line from the mid point of the diameter(point will be center of the circle) to the vertex that is making 90 degrees then it becomes the height(altitude).

So we can calculate the area of the traingle by (1/2)*height*hypotenuse.

So A is sufficient to calculate and i ended up here.

Please correct me if i am missing something here. thanks.

summer101 · Answer

Consider a triangle which is shown here: https://www.flickr.com/photos/janmr/6163380121/ Here height will not be line from the center to vertex.

shreyashree · Answer

Statement 1: Any triangle in a semicircle with the diameter as one of the sides would be a right triangle. However, this fact is not enough to find the area of the triangle. Not sufficient.

Statement 2: The triangle is isosceles only tells us that two angles of the triangle ABC are equal and nothing else. Not sufficient.

Combining: We see that triangle ABC is an isosceles right triangle. Using this we can determine that the base and height of the right triangle would be equal and we can use the value of the diameter = 2*10=20 to determine the other two sides (sides of a right isosceles triangle are in the ratio 1:1:\sqrt{2}).
Each of the other two sides would then equal 10\sqrt{2}

Area would be 05*10\sqrt{2}*10\sqrt{2}

Option C would be the answer.

hope this helps

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What is the area of the triangle ABC?

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What is the area of the triangle ABC?

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