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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 ...
We know that sum of two sides can not be greater than third side.Given that it is an isosceles triangle. now we can say that 4 can not be the third side because then 4+4<10. therefore="" 10="" would="" be="" the="" third="" side.="" hence="" semiperimeter="(10+10+4)/2" therefore="" 10="" would="" be="" the="" third="" side.="" hence="" semiperimeter="">
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Sahil has drawn an isosceles triangle. The length of two of the sides ...
The semiperimeter of a triangle
The semiperimeter of a triangle is defined as half of the sum of the lengths of all three sides of the triangle. It is denoted by the symbol 's'. Mathematically, it can be represented as:
s = (a + b + c)/2
where a, b, and c are the lengths of the sides of the triangle.
Given information
In this question, Sahil has drawn an isosceles triangle. An isosceles triangle has two sides of equal length. Let's denote the lengths of the two equal sides as a and b, and the length of the third side as c.
According to the given information, the lengths of the two equal sides are 4 cm and 10 cm. Therefore, a = b = 4 cm and c = 10 cm.
Calculating the semiperimeter
To calculate the semiperimeter of the triangle, we need to find the sum of the lengths of all three sides and divide it by 2.
s = (a + b + c)/2
s = (4 + 4 + 10)/2
s = 18/2
s = 9
Therefore, the semiperimeter of the triangle is 9 cm.
Answer
The correct answer is option B) 12 cm.
Explanation
The semiperimeter of a triangle can be calculated using the formula (a + b + c)/2, where a, b, and c are the lengths of the sides of the triangle. In this question, the lengths of the two equal sides are given as 4 cm and 10 cm. By substituting these values into the formula, we can calculate the semiperimeter as 9 cm. Therefore, the correct answer is option B) 12 cm, as it is the closest option to the calculated semiperimeter of 9 cm.
The semiperimeter of a triangle is defined as half of the sum of the lengths of all three sides of the triangle. It is denoted by the symbol 's'. Mathematically, it can be represented as:
s = (a + b + c)/2
where a, b, and c are the lengths of the sides of the triangle.
Given information
In this question, Sahil has drawn an isosceles triangle. An isosceles triangle has two sides of equal length. Let's denote the lengths of the two equal sides as a and b, and the length of the third side as c.
According to the given information, the lengths of the two equal sides are 4 cm and 10 cm. Therefore, a = b = 4 cm and c = 10 cm.
Calculating the semiperimeter
To calculate the semiperimeter of the triangle, we need to find the sum of the lengths of all three sides and divide it by 2.
s = (a + b + c)/2
s = (4 + 4 + 10)/2
s = 18/2
s = 9
Therefore, the semiperimeter of the triangle is 9 cm.
Answer
The correct answer is option B) 12 cm.
Explanation
The semiperimeter of a triangle can be calculated using the formula (a + b + c)/2, where a, b, and c are the lengths of the sides of the triangle. In this question, the lengths of the two equal sides are given as 4 cm and 10 cm. By substituting these values into the formula, we can calculate the semiperimeter as 9 cm. Therefore, the correct answer is option B) 12 cm, as it is the closest option to the calculated semiperimeter of 9 cm.
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Community Answer
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
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
Semiperimeter of the triangle = (4 + 10 + 10)/2 = 12 cm
Hence, option 2.
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
Semiperimeter of the triangle = (4 + 10 + 10)/2 = 12 cm
Hence, option 2.
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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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