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Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?
- a)9 cm
- b)12 cm
- c)1 or 2
- d)Cannot be determined
Correct answer is option 'B'. Can you explain this answer?
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Sahil has drawn an isosceles triangle. The length of two of the sides ...
Given triangle is an isosceles triangle.
The third side = 4 cm or 10 cm
The third side = 4 cm or 10 cm
For a triangle, sum of any two sides is greater than the third side.
4 cm cannot be the third side, as 4 + 4 < 10
We can check that for 4 cm, 10 cm and 10 cm, sum of any two sides is greater than the third side.
The third side = 10 cm
The third side = 10 cm
Semiperimeter of the triangle = (4 + 10 + 10)/2 = 12 cm
Hence, option 2.
Most Upvoted Answer
Sahil has drawn an isosceles triangle. The length of two of the sides ...
Solution:
An isosceles triangle has two sides equal in length.
Given, the length of two sides of the triangle is 4 cm and 10 cm.
Let the length of the third side be 'x'.
Since the triangle is isosceles, the third side will also be equal to either of the two sides.
Therefore, x = 4 cm or x = 10 cm.
Using the property of a triangle, the sum of any two sides of a triangle is always greater than the third side.
Therefore, 4 + 10 > x
=> 14 > x
Also, x + 4 > 10
=> x > 6
Therefore, the possible values of 'x' are 7, 8, or 9.
The semiperimeter of a triangle is given by the formula:
(semiperimeter) = (sum of all sides) / 2
Therefore, the semiperimeter of the triangle can be calculated as follows:
If x = 7, then semiperimeter = (4 + 7 + 10) / 2 = 21 / 2 = 10.5 cm
If x = 8, then semiperimeter = (4 + 8 + 10) / 2 = 22 / 2 = 11 cm
If x = 9, then semiperimeter = (4 + 9 + 10) / 2 = 23 / 2 = 11.5 cm
Therefore, the semiperimeter of the triangle can be either 10.5 cm, 11 cm, or 11.5 cm.
Hence, option B (12 cm) is not the correct answer.
Therefore, the answer is option D (Cannot be determined).
An isosceles triangle has two sides equal in length.
Given, the length of two sides of the triangle is 4 cm and 10 cm.
Let the length of the third side be 'x'.
Since the triangle is isosceles, the third side will also be equal to either of the two sides.
Therefore, x = 4 cm or x = 10 cm.
Using the property of a triangle, the sum of any two sides of a triangle is always greater than the third side.
Therefore, 4 + 10 > x
=> 14 > x
Also, x + 4 > 10
=> x > 6
Therefore, the possible values of 'x' are 7, 8, or 9.
The semiperimeter of a triangle is given by the formula:
(semiperimeter) = (sum of all sides) / 2
Therefore, the semiperimeter of the triangle can be calculated as follows:
If x = 7, then semiperimeter = (4 + 7 + 10) / 2 = 21 / 2 = 10.5 cm
If x = 8, then semiperimeter = (4 + 8 + 10) / 2 = 22 / 2 = 11 cm
If x = 9, then semiperimeter = (4 + 9 + 10) / 2 = 23 / 2 = 11.5 cm
Therefore, the semiperimeter of the triangle can be either 10.5 cm, 11 cm, or 11.5 cm.
Hence, option B (12 cm) is not the correct answer.
Therefore, the answer is option D (Cannot be determined).
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Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?a)9 cmb)12 cmc)1 or 2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?
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Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?a)9 cmb)12 cmc)1 or 2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?a)9 cmb)12 cmc)1 or 2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?a)9 cmb)12 cmc)1 or 2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?a)9 cmb)12 cmc)1 or 2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?a)9 cmb)12 cmc)1 or 2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sahil has drawn an isosceles triangle. The length of two of the sides of the triangle measure 4 cm and 10 cm. Which of the following is the semiperimeter of the triangle?a)9 cmb)12 cmc)1 or 2d)Cannot be determinedCorrect answer is option 'B'. Can you explain this answer?.
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