InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The length of the diagonals of a rhombus are 16cm and 12cm. The length of each side of the rhombus is(a) 8 cm (b) 9 cm (c) 10 cm (d) 12 cm |
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Answer» (c) 10 cm Explanation: Let ABCD be rhombus with AC and BD diagonals. Let AC and BD bisect at O. Therefore AO = 16/2=8 BO = 12/2=6cm In right angled triangle AOB, by Pythagoras theorem we can write as AB2=AO2+OB2 AB2=82+62 AB2= 64 + 36 AB= √ 100 AB =10 Length of rhombus is 10 cm |
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| 2. |
Two sides of a parallelogram are in the ratio 5:3. If its perimeter is 64cm, find the lengths of its sides. |
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Answer» Given that two sides of a parallelogram are in the ratio 5:3 so let x as common multiple. Also given that its perimeter is 64cm But we know that perimeter = 2 (length + width) = 2(5x + 3x) 64 = 2(5x + 3x) 64 = 2(8x) 64 = 16x x = 64/16 = 4 5x=20 3x=12 Therefore the sides are 20 and 12 |
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| 3. |
The length and breadth of a rectangle are in the ratio 4:3. If the diagonal measures 25cm then the perimeter of the rectangle is(a) 56 cm (b) 60 cm (c) 70 cm (d) 80 cm |
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Answer» (c) 70 cm Explanation: Given length and breadth of a rectangle are in the ratio 4:3 And diagonal= 25 cm Let ratio in multiple of x i.e. 4x and 3x According to the Pythagoras theorem we can write as (4x)2+(3x)2=252 16x2+9x2=625 25x2=625 X2=625/25=25 x=5 Length = 20 cm Breadth = 15 cm Perimeter= 2(l +b) = 2(20+15) = 2(35) = 70 cm |
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| 4. |
The perimeter of a parallelogram is 140cm. If one of the sides is longer than the other by 10cm, find the length of each of its sides. |
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Answer» Given that one of the sides is longer than the other by 10cm and let it be x and x+10 Also given that its perimeter is 140cm But we know that perimeter = 2 (length + width) = 2(x + (x + 10)) 140 = 2(2x + 10) 140 = 4x + 20 140 – 20 = 4x x = 120/4 = 30 x=30cm x + 10 = 40cm Therefore the sides are 30cm and 40cm. |
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| 5. |
Two sides of a parallelogram are in the ratio 5 : 3. If its perimeter is 64 cm, find the lengths of its sides. |
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Answer» Let x be the common multiple. According to question, sides will be 5x and 3x. Perimeter = \(2(l+w)\) 64 = 2 (5x + 3x) 64 = 16x x = 4 5x = 20 cm 3x = 12 cm So, sides will be 20 cm and 12 cm. |
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| 6. |
The sides of a rectangle are in the ratio 5 : 4 and its perimeter is 90 cm. Find its length and breadth. |
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Answer» Let x be the common multiple. Length = 5x Breadth = 4x Perimeter = \(2(l+w)\) 90 = 2 (5x + 4x) 18x = 90 X = 5 Length = 5x = 25 cm Breadth = 4x = 20 cm |
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| 7. |
In the given figure ABCD is a square. Find the measure of ∠CAD. |
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Answer» Let \(\angle\)CAD be x. ABCD is a square. So, DA = DC (every side of square is equal) Therefore, ∠ACD = ∠CAD = x° ∠ACD + ∠CAD + ∠ADC= 180° (ACD is right angled triangle) x° + x° + 90° = 180° 2 x° = 90° x° = 45° |
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