In the figure given below, the radius of the inscribed circle with the centre O is 10 cm. If the triangle ABC is equilateral and its side is a, find the area of triangle ABC (in cm2 ). Please note that AB, BC and CA are tangential to the circle.
Answer: A Given the radius of triangle ABC i.e OD = 10 cm.
Since, Triangle ABC is an equilateral, then AD = 3(OD) AD = 3* 10 = 30 cm. Now, in right angled triangle ABD a2 - a2 /4 = (30)2 => a = 20√3 Area of an equilateral triangle = √3/4 * a2 Area = 300√3 = 519.6 cm2
Q. No. 38:
A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following must be true ?
Answer: B Let the length of circuit be l. 2(l+w) = p........(i) And, lw = k => l = k/w.......(ii) From both the equations, 2(k/w + w) = p 2(k + w2 ) = pw 2w2 + 2k - pw = 0.
Q. No. 39:
In the figure above, ABCD is a regular rectangle and its length is twice its width. If the area of triangle EAB is 144 cm2. What is the length of the rectangle?
Answer: D As all of them have same base so they have same radius. Suppose their radius is r and height is h. Curved surface area of cylinder = 2πrh = 2πr2 Curved surface area of hemisphere = 2πr2 Curved surface area of cone = πr(r2 +h2 )1/2 = πr2√2 Ratio between them = 2πr2 : 2πr2 : πr2√2 = √2 : √2 : 1
