Discussion
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- Question
- 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?
Options- A. 4 cm
- B. 5 cm
- C. 6 cm
- D. 7 cm
- Correct Answer
- 5 cm
Explanation? s= (13 + 5 + 12) / 2 cm
= 15cm
s-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 - 1. Area of a square with side x is equal to the area of a triangle with base x. The altitude of the triangle is?
Options- A. x/2
- B. x
- C. 2x
- D. 4x Discuss
- 2. If the circumference of a circle is the 352 meters, then its area in m square is?
Options- A. 9856
- B. 8956
- C. 6589
- D. 5986 Discuss
- 3. The area of circle is 38.5 sq. cm. Its circumference is?
Options- A. 6.20 cm
- B. 11 cm
- C. 22 cm
- D. 121 cm Discuss
- 4. The area of a circular field is 13.86 hectares . The cost of fencing it at the rate of 20 paisa per meter is?
Options- A. Rs. 277.20
- B. Rs. 264
- C. Rs. 324
- D. Rs. 198 Discuss
- 5. The difference between the circumference and the radius of a circle is 37 cm. The area of a circle is?
Options- A. 148 sq. cm
- B. 111 sq. cm
- C. 154 sq. cm
- D. 259 sq. cm Discuss
- 6. The perimeter of an isosceles triangle is equal to 14 cm . The lateral side is to the base in the ratio 5 : 4 the area of the triangle is?
Options- A. 1/2?21 cm2
- B. 3/2?21 cm2
- C. ?212
- D. 2?21 cm2 Discuss
- 7. The sides of a triangular board are 13 meters, 14 meters and 15 meters. The cost of paining it at the rate of Rs. 8.75 per m 2 is?
Options- A. Rs. 688.80
- B. Rs. 735
- C. Rs. 730.80
- D. Rs. 722.50 Discuss
- 8. If the diagonal of a square is double, how does the area of the square change?
Options- A. Becomes four fold
- B. Becomes three fold
- C. Becomes two fold
- D. None of the above Discuss
- 9. A circle and a square have same area. The ratio of the side of the square and the radius of the circle is?
Options- A. ?? : 1
- B. 1 : ??
- C. 1 : ?
- D. ? : 1 Discuss
- 10. 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?
Options- A. 29.46 km/hr.
- B. 31.68 km/hr.
- C. 36.25 km/hr.
- D. 32.72 km/hr. Discuss
Area problems
Search Results
Correct Answer: 2x
Explanation:
Let h be the altitude of triangle.
So area of triangle = (1/2)xh
area of square = x2
From question area of square = area of triangle
x2 = (1/2)xh
? h = (2x2)/x = 2x
Correct Answer: 9856
Explanation:
circumference = 2?r = 2 x (22 / 7) x r = 352
? r = (352 x 7) / (22 x 2) =56 cm
Now area = ?r2 = (22 / 7) x 56 x 56 m2
= 9856 m2
Correct Answer: 22 cm
Explanation:
? ( 22 x r2) / 7 = 38.5
? r2 =(38.5 x 7) /22
? r = 3.5 cm
? Circumference = 2 x (22/7) x 3.5 cm
= 22 cm
Correct Answer: Rs. 264
Explanation:
? 22/7 x r2 = 13.86 x 10000
? r2 = (13.86 x 10000 x 7) / 22
? r = 210 m
? Circumference = [2 x (22/7) x 210 ] m
= 1320 m
Cost of fencing = Rs. (1320 x 20)/100
= Rs . 264
Correct Answer: 154 sq. cm
Explanation:
? 2?r - r = 37
? [(2 x 22/7) -1]r= 37
? 37r / 7= 37
? r = 7
So, area of the circle =(22/7) x 7 x 7 cm2
= 154 cm2
Correct Answer: 2?21 cm2
Explanation:
Let lateral side = (5y) cm and base = (4y) cm
? perimeter = 5y + 5y + 4y = 14
?y = 1
So, the sides are 5 cm , 5 cm and 4 cm
Now s= 1/2 (5 + 5 + 4) cm = 7 cm
(s-a) = 2 cm
(s-b) = 2 cm and
(s-c) = 3 cm
? Required Area = ? (7 x 2 x 2 x 3) cm2
=2?21 cm2
Correct Answer: Rs. 735
Explanation:
s = (13 + 14 + 15 ) / 2 = 21,
s-a = 8 ,
s-b = 7,
s-c= 6
? Area to be painted = ? [s(s-a) (s-b) (s-c)]
=? [21 x 8 x 7 x 6] m2
= 84 m2
? Cost of painting = Rs. (84 x 8.75) = Rs. 735
Correct Answer: Becomes four fold
Explanation:
Ratio of the areas = area of original square / area of new square
= [ d2 / 2 ] / [ (2d)2 / 2 ] = 1/4
? New area becomes 4 fold.
Correct Answer: 1 : ??
Explanation:
? Area of square = Area of circle
? x2 = ?r2
? x/r = ??
= ? ? : 1
Correct Answer: 31.68 km/hr.
Explanation:
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
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