Area Problems The area of circle inscribed in an equilateral triangle is 462 cm . The perimeter of the triangle is? 72.6 cms 42 ? 3 cms 126 cms 168 cms 72.6 cms 42 ? 3 cms 126 cms 168 cms ANSWER EXPLANATION DOWNLOAD EXAMIANS APP ? 22/7 x r2 = 462? r2 = (462 x 7) /22 = 147? r = 7?3 cm ? Height of the triangle = 3r = 21?3 cmNow, ? a2 = a2/4 + (3r)2? 3a2/4 = (21?3)2? a2 = (1323 x 4)/3? a = 21x 2 = 42 cm? Perimeter = 3a = 3 x 42=126 cm
Area Problems Angles of a quadrilateral are in the ratio 3 : 4 : 5 : 8. The smallest angle is 40° 18° 36° 54° 40° 18° 36° 54° ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let First angle = 3kSecond angle = 4kThird angle = 5k and Fourth angle = 8kWe know 3k + 4k + 5k + 8k = 360°? 20k = 360° ? k = 18 °Measure of smallest angle = 3k =3 x 18 ° = 54 °
Area Problems In a triangle ABC, BC = 5 cm AC = 12 cm and AB = 13 cm. The length of a altitude drawn from B on AC is? 6 cm 7 cm 4 cm 5 cm 6 cm 7 cm 4 cm 5 cm ANSWER EXPLANATION DOWNLOAD EXAMIANS APP ? s= (13 + 5 + 12) / 2 cm = 15cms-a = 2 cm, s-b = 10 cm and s-c = 3 cm ? Area = ? (15 x 2 x 10 x 3 ) cm2= 30 cm2? (12 x h) / 2 = 30 ? h = 5 cm
Area Problems The radius of the wheel of a vehicle is 70 cm. The wheel makes 10 revolutions in 5 seconds. The speed of the vehicle is? 29.46 km/hr. 32.72 km/hr. 36.25 km/hr. 31.68 km/hr. 29.46 km/hr. 32.72 km/hr. 36.25 km/hr. 31.68 km/hr. ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Circumference = 2?r = 2 x (22 / 7) x 70 cm = 440 cm Distance travelled in 10 revolutions = 440 x 10 cm = 4400 cm = 44 m? Speed = distance / time= 44 / 5 m/sec= (44 / 5) x (18 / 5) km/hr = 31.68 km/hr
Area Problems The ratio between the length and breadth of a rectangular field is 5:4. If the breadth is 20 meters less than the length, the perimeters of the field is? 360 m 280 m none of these 260 m 360 m 280 m none of these 260 m ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Let length of rectangular field = 5y,so width = 4y.From question5y - 4y = 20m? x = 20m ? Length = (5 x 20)m = 100 mBreadth = (4 x 20) m = 80 m ? Perimeter = 2 (100 + 80 ) m = 360 m
Area Problems If the radius of a circle be reduced by 50%. Its area is reduced by? 65.5% 31.5% 34.5% 39.5% 65.5% 31.5% 34.5% 39.5% ANSWER EXPLANATION DOWNLOAD EXAMIANS APP Original area = ? x (r/2)2 = ?r2/4Reduction in area = ? r2 - 3? r2/4? Reduction per cent = [ 3?r2/4 x 4/(?r2) x 100 ] %= 75%
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