Discussion
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- Question
- A square, a circle and equilateral triangle have same perimeter.
Consider the following statements.
I. The area of square is greater than the area of the triangle.
II. The area of circle is less then the area of triangle.
Which of the statement is/are correct?
Options- A. Only I
- B. Only II
- C. Both I and II
- D. Neither I nor II
- Correct Answer
- Only I
ExplanationLet the radius of circle is 'r' and a side of a square is 'a',
then given condition
2?r = 4a
? a = ?r/2
? Area of square = (?r/2)2 = ?2 /4r2 = 9.86r2/4 = 2.46r2
and area of circle = ?r2 = 3.14;r2
and let the side of equilateral triangle is x.
Then, given condition,
3x = 2?r
? x = 2?r/3
? Area of equilateral triangle = ?3/4 x 2
= ?3/4 x 4?2r2/9
= ?2/3?3r2
= 1.89r2
Hence, Area of circle > Area of square > Area of equilateral triangle. - 1. A polygon has 44 diagonals the number of its sides is?
Options- A. 9
- B. 10
- C. 11
- D. 12 Discuss
- 2. The ratio of the corresponding sides of two similar triangles is 3 : 4, The ratio of their areas is?
Options- A. 4 : 3
- B. 3 : 4
- C. 9 : 16
- D. ? 3: 2 Discuss
- 3. A room 5.44 m x 3.75 m is to be paved with square tiles. the least number of tiles required to cover the floor is?
Options- A. 162
- B. 176
- C. 184
- D. 192 Discuss
- 4. A park is in the form of a square one of whose sides is 100 m . The area of the park excluding the circular lawn in the centre of the park is 8614 m 2. The radius of the circular lawn is?
Options- A. 21 m
- B. 31 m
- C. 41 m
- D. None of these Discuss
- 5. The area of circle inscribed in an equilateral triangle is 462 cm . The perimeter of the triangle is?
Options- A. 42 ? 3 cms
- B. 126 cms
- C. 72.6 cms
- D. 168 cms Discuss
- 6. If the area of an equilateral triangle is x and its perimeter is y, then which one of the following is correct?
Options- A. y4 = 432 x2
- B. y4 = 216 x2
- C. y2 = 432 x2
- D. None of these Discuss
- 7. The area of circle inscribed in an equilateral triangle is 154 sq cm. What is the perimeter of the triangle?
Options- A. 21 cm
- B. 42?3 cm
- C. 21?3 cm
- D. 42 cm Discuss
- 8. The length of a rectangle is twice its breadth. If its length is decreased half of the 10 cm and the breadth is increased by half of the 10 cm cm, the area of the rectangle is increased by 5 sq cm, more than 70 sq cm. Find the length of the rectangle.
Options- A. 30 cm
- B. 40 cm
- C. 21 cm
- D. 45 cm Discuss
- 9. The area of rectangle is 1.8 times the area of a square. The length of the rectangle is 5 times the breadth. The side of the square is 20 cm. What is the perimeter of the rectangle?
Options- A. 145 cm
- B. 144 cm
- C. 133 cm
- D. 135 cm Discuss
- 10. How many circular plates of diameter d be taken out of a square plate of side 2d with minimum loss of material?
Options- A. 8
- B. 6
- C. 5
- D. 2 Discuss
Area problems
Search Results
Correct Answer: 11
Explanation:
Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by talking 2 at a time is nC2
These nC2 lines also include n sides of polygon.
Therefore, the number of diagonals formed is nC2 - n.
Thus, nC2 - n = 44
? [n(n - 1)/2] - n = 44
? ( n2 - 3n) / 2 = 44
? n2 - 3n = 88
? n2 - 3n - 88 = 0
?(n - 11) (n + 8) = 0
? n = 11
Correct Answer: 9 : 16
Explanation:
Ratio of similar triangle
= Ratio of the square of corresponding sides
= (3x)2 / (4x)2 = 9x2 / 16x2
= 9/16 = 9 : 16
Correct Answer: 176
Explanation:
Area of the room =(544 x 374) cm2
size of largest square tile = H.C.F. of 544 & 374
= 34 cm
Area of 1 tile = (34 x 34) cm2
? Least number of tiles required
= (544 x 374) / (34 x 34) = 176
Correct Answer: 21 m
Explanation:
Area of park = 100 x 100 = 10000 m2
Area of circular lawn = Area of park - area of park excluding circular lawn
= 10000 - 8614
= 1386
Now again area of circular lawn = (22/7) x r2 = 1386 m2
? r2 = (1386 x 7) / 22
= 63 x 7
= 3 x 3 x 7 x 7
? r = 21 m
Correct Answer: 126 cms
Explanation:
? 22/7 x r2 = 462
? r2 = (462 x 7) /22 = 147
? r = 7?3 cm
? Height of the triangle = 3r = 21?3 cm
Now, ? 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
Correct Answer: y4 = 432 x2
Explanation:
Area of equilateral triangle = ?3a2/4 = x ......(i)
And perimeter = 3a = y
? a = y/3 ....(ii)
Now, Putting the value of a from Eq. (ii) in Eq. (i). we get
?3 (y/3)2/4 = x
? x = ?3 x y2/36
? x = y2/3?3x = y2/12?3
12?3 x = y2
On squaring both sides, we get
y4 = 432x2
Correct Answer: 42?3 cm
Explanation:
We know that, the radius of a circle inscribed in a equilateral triangle = a/[2?3]
Where, a be the length of the side of an equilateral triangle.
Given that, area of a circle inscribed in an equilateral tringle = 154 cm2
? ?(a/2?3)2 = 154
? (a/2?3)2 = 154 x (7/22) = (7)a2
? a = 42?3 cm
Perimeter of an equilateral triangle = 3a
= 3(14?3)
= 42?3 cm
Correct Answer: 40 cm
Explanation:
Given that, l = 2b [Here l = length and b = breadth]
Decrease in length = Half of the 10 cm = 10/2 = 5 cm
Increase in breadth = Half of the 10 cm = 10/2 = 5 cm
Increase in the area = (70 + 5) = 75 sq cm
According to the question,
(l - 5) (b + 5) = lb + 75
? (2b - 5) (b + 5) = 2b2 + 75 [since l = 2b]
? 5b - 25 = 75
? 5b = 100
? b = 100/ 5 = 20
? l = 2b = 2 x 20 = 40 cm
Correct Answer: 144 cm
Explanation:
Area of square = (Side)2 = 202
= 400 sq cm
? Area of rectangle
= 1.8 x 400 = 720 sq cm
Let length and breadth of rectangle be 5k and k respectively.
Then, according to the question,
5k x k = 720
? 5k2 = 720
? k2 = 720/5 = 144
? k = ?144 = 12 cm
Perimeter of rectangle = 2(5k + k) = 12k
= 12 x12 = 144 cm
Correct Answer: 5
Explanation:
Area of square plate = (Side)2
= (2d)2
= 4d2
Area of circular plate = ? (d/2)2
= ?d2/4
? Number of square plates
= [(4d2)/4] / [(?d2)/4]
= (4 x 4)/?
? 5
Since, nearest integer value is 5.
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