What is the perimeter of the triangle ABC? One of its side is 10√3 units. A. BC is the hypotenuse of the right angle triangle ABC. B. The sum of the areas of the semicircles described on the three sides of the triangle ABC is 100 π sq. units. Options: A . &nbspStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient B . &nbspStatement (2) ALONE is sufficient, but statement (1) alone is not sufficient C . &nbspEach statement alone is sufficient D . &nbspBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. E . &nbspStatement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer: Option D : D Option (d ) Given, sum of areas of semi-circles x, y and z is 100π If BC = a cm, AC = b cm, AB = c cm. Area of semi-circle x is π/2 x a 2 /4 cm2 Area of semi circle y is π/2 x c 2 /4 cm2 Area of semi circlezx is π/2 x b 2 /4 cm2 ½ π/4 (a 2 + b 2 +c 2 ) =100π a 2 + b 2 + c 2 = 800 from Statement 1:We know that in ABC is a right angle triangle. a 2 = b 2 +c 2 = 2(b 2 +c 2 ) = 800 b 2 +c 2 = 400 b 2 +c 2 = a 2 = 400 ;a = 20 b or c = 10√3 and the sides are 10, 10√3, 20 the perimeter = 30 + 10√3 cm

What is the perimeter of the triangle ABC? One of its side is 10√3 units.

Question

What is the perimeter of the triangle ABC? One of its side is 10√3 units.
A. BC is the hypotenuse of the right angle triangle ABC.
B. The sum of the areas of the semicircles described on the three sides of the triangle ABC is 100 π sq. units.

Options:

A . Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

B . Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient

C . Each statement alone is sufficient

D . BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

E . Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.

Answer: Option D
:
D
Option (d)Given, sum of areas of semi-circles x, y and z is 100πIf BC = a cm, AC = b cm, AB = c cm.Area of semi-circle x is π/2 x a²/4 cm2Area of semi circle y is π/2 x c²/4 cm2Area of semi circlezx is π/2 x b²/4 cm2½ π/4 (a² + b² +c²) =100πa2 + b² + c² = 800from Statement 1:We know that in ABC is a right angle triangle.a² = b² +c² = 2(b² +c²) = 800b² +c² = 400b² +c² = a² = 400 ;a = 20b or c = 10√3 and the sides are 10, 10√3, 20the perimeter = 30 + 10√3 cm

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