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If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle?
Verified Answer
If the difference between the semi-perimeter and the sides of triangle...
Let the semi-perimeter of the triangle be s.
Let the sides of the triangle be a, b and c.
Given: s – a = 8, s – b = 7 and s – c = 5
Adding all the above equations, we get
(s – a) + (s – b) + (s – c) = 8 + 7 + 5
⇒ 3s – (a + b + c) = 20
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If the difference between the semi-perimeter and the sides of triangle...
Solution:
Given:
Difference between the semi-perimeter and the sides of triangle ABC:
AB - s = 8 cm
BC - s = 7 cm
CA - s = 5 cm
To find the area of triangle ABC, we need to know the lengths of its sides. Let's solve for the lengths of AB, BC, and CA.
Solving for AB:
AB - s = 8 cm
AB = 8 cm + s
Solving for BC:
BC - s = 7 cm
BC = 7 cm + s
Solving for CA:
CA - s = 5 cm
CA = 5 cm + s
Now, we can use the formula for the area of a triangle, which is given by Heron's formula:
Area = sqrt(s * (s - AB) * (s - BC) * (s - CA))
where s is the semi-perimeter and AB, BC, and CA are the lengths of the sides.
Calculating the semi-perimeter (s):
The semi-perimeter is the sum of the lengths of the sides divided by 2.
s = (AB + BC + CA) / 2
Substituting the values of AB, BC, and CA:
s = (8 cm + s + 7 cm + s + 5 cm + s) / 2
s = (20 cm + 3s) / 2
2s = 20 cm + 3s
2s - 3s = 20 cm
-s = 20 cm
s = -20 cm (rejected, as length cannot be negative)
Therefore, there is no valid solution for the given lengths of AB, BC, and CA.
Conclusion:
Based on the given information, it is not possible to find the area of triangle ABC. Please recheck the lengths of the sides or provide additional information.
Given:
Difference between the semi-perimeter and the sides of triangle ABC:
AB - s = 8 cm
BC - s = 7 cm
CA - s = 5 cm
To find the area of triangle ABC, we need to know the lengths of its sides. Let's solve for the lengths of AB, BC, and CA.
Solving for AB:
AB - s = 8 cm
AB = 8 cm + s
Solving for BC:
BC - s = 7 cm
BC = 7 cm + s
Solving for CA:
CA - s = 5 cm
CA = 5 cm + s
Now, we can use the formula for the area of a triangle, which is given by Heron's formula:
Area = sqrt(s * (s - AB) * (s - BC) * (s - CA))
where s is the semi-perimeter and AB, BC, and CA are the lengths of the sides.
Calculating the semi-perimeter (s):
The semi-perimeter is the sum of the lengths of the sides divided by 2.
s = (AB + BC + CA) / 2
Substituting the values of AB, BC, and CA:
s = (8 cm + s + 7 cm + s + 5 cm + s) / 2
s = (20 cm + 3s) / 2
2s = 20 cm + 3s
2s - 3s = 20 cm
-s = 20 cm
s = -20 cm (rejected, as length cannot be negative)
Therefore, there is no valid solution for the given lengths of AB, BC, and CA.
Conclusion:
Based on the given information, it is not possible to find the area of triangle ABC. Please recheck the lengths of the sides or provide additional information.
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If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle?
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If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle?.
If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the difference between the semi-perimeter and the sides of triangle ABC are 8cm, 7cm and 5cm respectively, then find the area of the triangle?.
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