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The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is?
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The sides of an equilateral triangle are shortened by 12, 13,and 14 un...
Problem Statement:
The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is?
Solution:
Let the side of the equilateral triangle be x units.
Then, the sides of the right-angled triangle will be:
- x - 12 units
- x - 13 units
- x - 14 units
According to the Pythagorean theorem:
(x - 14)2 + (x - 13)2 = (x - 12)2
Simplifying the above equation:
- x2 - 28x + 196 + x2 - 26x + 169 = x2 - 24x + 144
- 2x2 - 78x + 521 = 0
Using the quadratic formula:
- x = (78 ± sqrt(782 - 4(2)(521))) / (2(2))
- x = (78 ± sqrt(36)) / 4
- x = (78 ± 6) / 4
Therefore, the side of the equilateral triangle can be:
- x = 21 units
- x = 9/2 units (rejected as it is less than the sum of the other two sides)
Answer:
Therefore, the side of the equilateral triangle is 21 units.
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The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is?
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The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is?.
The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of an equilateral triangle are shortened by 12, 13,and 14 unit respectively and a right angle triangle is formed. The side of the equilateral triangle is?.
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