Area problems
- 1. The sides of a triangle area in the ratio of 1/3 : 1/4 : 1/5 and its perimeter is 94 cm.
Find the length of the smallest side of the triangle .
Options- A. 18 cm
- B. 22.5 cm
- C. 24 cm
- D. 27 cm Discuss
Correct Answer: 24 cm
Explanation:
Given ratio = 1/3 : 1/4 : 1/5 = 20 : 15 : 12
Let length of the sides be 20k, 15k and 12k.
Then, according to the question,
20k + 15k + 12k = 94
? 47k = 94
? k = 94/47 = 2
Smallest side = 12k = 12 x 2 = 24 cm
- 2. The perimeter of an equilateral triangle is 90 cm. Find its area.
Options- A. 225?3 sq cm
- B. 250?3 sq cm
- C. 135?3 sq cm
- D. 151?3 sq cm Discuss
Correct Answer: 225?3 sq cm
Explanation:
Given that, perimeter = 90 cm
? 3a = 90 cm [a = side]
? a = 90/3 = 30 cm
? Area = ?3a2 / 4 = ?3/4 x (30)2
= 900 x ?3/4 = 225?3 sq cm
- 3. The area of an equilateral triangle is ? 243 /4 sq cm. Find the length of its side.
Options- A. 3 cm
- B. 3?3 cm
- C. 9 cm
- D. ?3 cm Discuss
Correct Answer: 3 cm
Explanation:
According to the question,
area = ?3a2/4
= ?243 /4
? a2 = ?81 x 3/?3
? a = ?9
= 3 cm
- 4. The diagonals of a squares is 4?2 cm. The diagonal of another square whose area is double that of the first square is
Options- A. 8 cm
- B. 8?2 cm
- C. 4?2 cm
- D. 6 cm Discuss
Correct Answer: 8 cm
Explanation:
Diagonal of square = ?2a [a = side]
4?2 = ?2 a
a = 4 cm
Now, area of square = a2 = (42) = 16
Side of a square whose area is 2 x 16.
a12 = 32
? a1 = ?32 ?a14?2
Now, diagonal of new square = ?2a
= ?2x 4 ?2
= 8 cm
- 5. The diagonals of two squares are in the ratio of 3 : 2. Find the ratio of their areas.
Options- A. 9 : 4
- B. 9 : 2
- C. 9 : 5
- D. 9 : 7 Discuss
Correct Answer: 9 : 4
Explanation:
Let the diagonals of the squares be 3x and 2x.
? Ratio of their areas = [(1/2) (3x2)] / [(1/2) (2x2)] = 9/4
- 6. If the sides of a squares is increased by 25%, then the area of the squares will be increased by
Options- A. 125%
- B. 50%
- C. 56.25%
- D. 53.75% Discuss
Correct Answer: 56.25%
Explanation:
Required increment = 2a + [a2 / 100] %
= 2 x 25 + [(252)/100)] %
= 50 + (625/100)%
= 56.25%
- 7. The perimeter of two square is 12 cm and 24 cm. The area of the bigger square is how many times that of the smaller?
Options- A. 2 times
- B. 3 times
- C. 4 times
- D. 5 times Discuss
Correct Answer: 4 times
Explanation:
Ratio of area of 2 squares = (ratio of perimeter of 2 squares)2
= (24/12)2
= 4
- 8. A cost of cultivating a square field at a rate of ? 135 per hectare is ? 1215. The cost of putting a fence around it at the rate of 75 paise per meter wouldbe
Options- A. ? 360
- B. ? 810
- C. ? 900
- D. ? 1800 Discuss
Correct Answer: ? 900
Explanation:
Area of the field =1215/135 = 9 hec
= 90000 m2 [1 hec =10000 m2]
? Side of the field = ?90000 = 300 m
Perimeter of the field = 4 x 300 = 1200 m
Now, cost of putting a fence around field = (1200 x 75)/100 = ? 900
- 9. Diagonals of a rhombus area 1 m and 1.5 m in lengths. The area of the rhombus is
Options- A. 0.75 m2
- B. 1.5 m2
- C. 1.5 m2
- D. 0.375 m2 Discuss
Correct Answer: 0.75 m2
Explanation:
Area of rhombus =(d1 x d2)/2
=(1 x 1.5)/2 m2
= 0.75 m2
- 10. If the diagonals of a rhombus are 4.8 cm 1.4 cm, then what is the perimeter of the rhombus?
Options- A. 5 cm
- B. 10 cm
- C. 12 cm
- D. 20 cm Discuss
Correct Answer: 10 cm
Explanation:
Perimeter of rhombus
= 2 ? d1 2 + d2 2
= 2 ?(4.8)2 + (1.4)2
= 2 ?23.04 + 1.96
= 2 ?25
= 2 x 5 = 10 cm
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