Please review this question once again. I am bit confused by the date presented by you.
In the triangle ABC, angle A is 30 degrees, and AD is perpendicular to AC ( how can AD be perpendicular to AC, as per the diagram presented by you).
What is the perimeter of the triangle ( which triangle you are talking about - there are 3 triangles )?
geometry
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I think it is BD perpendicular to AC. We have to find the perimeter of triangle ABC.sud21 wrote:In the triangle ABC, angle A is 30 degrees, and AD is perpendicular to AC. What is the perimeter of the triangle?
1). given the perimeter of the triangle ABD.
2). Given the perimeter of the triangle BCD.
(1) We are given the perimeter of triangle ABD but that is NOT sufficient to find the perimeter of triangle ABC.
(2) We are given the perimeter of the triangle BCD but again that is NOT sufficient to find the perimeter of triangle ABC.
Combining (1) and (2), we know the perimeters of two triangles, ABD and BCD but for the perimeter of triangle ABC, we need to subtract the length of BD, which is not known; NOT sufficient.
The correct answer is E.
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ArunangsuSahu
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I think it is BD perpendicular to AC.
so when BD is perpendicular to AC angle BDC = angle BDA = 90 degree.
Now taking triangle BDC, angle A=30 degrees(given) ; D =90(perpendicular).
Now, sum angle property gives angle B = 60. Therefore, it is a 30,60,90 triangle which gives us opposite sides to the angles as 1, root3, 2 respectively. so perimeter is given as 3+root3.
Now perpendicular BD divides AC into 2 equal parts. Therefore, DC=root3.
Also, in triangle BDC angle D=90 degree(perpendicular).
Now applying pythagoran theorem gives us BC=1+3=4.
Therefore, perimeter of triangle ABC gives us AB=2, AC=2root3, BC=4. Therefore perimeter ABC=6+2root3
THEREFORE (A) IS SUFFICIENT.
OPTION (B) IS INSUFFICIENT BECAUSE WE CAN'T FIND BC, WE CAN ONLY SAY DC=X/2.
SO ANSWER (A). LET ME KNOW IF I AM RIGHT.
so when BD is perpendicular to AC angle BDC = angle BDA = 90 degree.
Now taking triangle BDC, angle A=30 degrees(given) ; D =90(perpendicular).
Now, sum angle property gives angle B = 60. Therefore, it is a 30,60,90 triangle which gives us opposite sides to the angles as 1, root3, 2 respectively. so perimeter is given as 3+root3.
Now perpendicular BD divides AC into 2 equal parts. Therefore, DC=root3.
Also, in triangle BDC angle D=90 degree(perpendicular).
Now applying pythagoran theorem gives us BC=1+3=4.
Therefore, perimeter of triangle ABC gives us AB=2, AC=2root3, BC=4. Therefore perimeter ABC=6+2root3
THEREFORE (A) IS SUFFICIENT.
OPTION (B) IS INSUFFICIENT BECAUSE WE CAN'T FIND BC, WE CAN ONLY SAY DC=X/2.
SO ANSWER (A). LET ME KNOW IF I AM RIGHT.
