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If the base of an isosceles ΔABC is 48 cm and its area is 168 cm2, then what is the length of one of its equal sides?
- a)8 cm
- b)15 cm
- c)17 cm
- d)25 cm
Correct answer is option 'D'. Can you explain this answer?
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If the base of an isosceles ΔABC is 48 cm and its area is 168 cm...
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If the base of an isosceles ΔABC is 48 cm and its area is 168 cm...
Understanding the Problem
To find the length of one of the equal sides of isosceles triangle ABC, we have:
- Base (BC) = 48 cm
- Area = 168 cm²
Area of Triangle Formula
The area (A) of a triangle can be calculated using the formula:
A = (1/2) × base × height
Where:
- Base = length of the triangle's base
- Height = perpendicular distance from the apex to the base
Calculating Height
We can rearrange the area formula to solve for height (h):
h = (2 × Area) / base
Substituting the values:
h = (2 × 168) / 48
h = 336 / 48
h = 7 cm
Applying Pythagorean Theorem
In isosceles triangle ABC, we can find the length of one of the equal sides (let's call it 's') using the Pythagorean theorem.
- The height divides the base into two equal parts, so each part (half the base) = 24 cm.
- We now have a right triangle with:
- One leg = height = 7 cm
- Other leg = half of the base = 24 cm
Using the Pythagorean theorem:
s² = (24)² + (7)²
s² = 576 + 49
s² = 625
s = √625
s = 25 cm
Conclusion
Thus, the length of one of the equal sides of triangle ABC is:
25 cm
Therefore, the correct answer is option 'D'.
To find the length of one of the equal sides of isosceles triangle ABC, we have:
- Base (BC) = 48 cm
- Area = 168 cm²
Area of Triangle Formula
The area (A) of a triangle can be calculated using the formula:
A = (1/2) × base × height
Where:
- Base = length of the triangle's base
- Height = perpendicular distance from the apex to the base
Calculating Height
We can rearrange the area formula to solve for height (h):
h = (2 × Area) / base
Substituting the values:
h = (2 × 168) / 48
h = 336 / 48
h = 7 cm
Applying Pythagorean Theorem
In isosceles triangle ABC, we can find the length of one of the equal sides (let's call it 's') using the Pythagorean theorem.
- The height divides the base into two equal parts, so each part (half the base) = 24 cm.
- We now have a right triangle with:
- One leg = height = 7 cm
- Other leg = half of the base = 24 cm
Using the Pythagorean theorem:
s² = (24)² + (7)²
s² = 576 + 49
s² = 625
s = √625
s = 25 cm
Conclusion
Thus, the length of one of the equal sides of triangle ABC is:
25 cm
Therefore, the correct answer is option 'D'.
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Question Description
If the base of an isosceles ΔABC is 48 cm and its area is 168 cm2, then what is the length of one of its equal sides?a)8 cmb)15 cmc)17 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer? for CTET & State TET 2025 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about If the base of an isosceles ΔABC is 48 cm and its area is 168 cm2, then what is the length of one of its equal sides?a)8 cmb)15 cmc)17 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the base of an isosceles ΔABC is 48 cm and its area is 168 cm2, then what is the length of one of its equal sides?a)8 cmb)15 cmc)17 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer?.
If the base of an isosceles ΔABC is 48 cm and its area is 168 cm2, then what is the length of one of its equal sides?a)8 cmb)15 cmc)17 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer? for CTET & State TET 2025 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about If the base of an isosceles ΔABC is 48 cm and its area is 168 cm2, then what is the length of one of its equal sides?a)8 cmb)15 cmc)17 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the base of an isosceles ΔABC is 48 cm and its area is 168 cm2, then what is the length of one of its equal sides?a)8 cmb)15 cmc)17 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer?.
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