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.

• 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 1

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

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 a²/4 cm2

Area of semi circle y is π/2 x c²/4 cm2

Area of semi circlezx is π/2 x b²/4 cm2

½ π/4 (a² + b² +c²) =100π

a2 + b² + c² = 800

from Statement 1:We know that in ABC is a right angle triangle.

a² = b² +c² = 2(b² +c²) = 800

b² +c² = 400

b² +c² = a² = 400 ;a = 20

b or c = 10√3 and the sides are 10, 10√3, 20

the perimeter = 30 + 10√3 cm