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An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, but the area of triangle remains the same. Find the base and altitude of the triangle respectively.
- a)100 cm, 24 cm
- b)24 cm, 10 cm
- c)20 cm, 12 cm
- d)12 cm, 20 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
An altitude of a triangle is five-thirds the length of its correspondi...
Let the base be x
Altitude -
∴ Altitude = 12 × 5/3 = 20 cm
Altitude -
∴ Altitude = 12 × 5/3 = 20 cm
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Most Upvoted Answer
An altitude of a triangle is five-thirds the length of its correspondi...
Let's assume that the base of the triangle is 'b' cm and the altitude is 'h' cm.
Given that the altitude is five-thirds the length of the base, we can write the equation as:
h = (5/3)b
Since the area of a triangle is given by the formula: area = (1/2) * base * altitude, we can write the equation as:
(1/2) * b * h = area
Since the area remains the same, even after the changes in altitude and base, we can write the equation as:
(1/2) * (b - 2) * (h + 4) = (1/2) * b * h
Simplifying the equation, we get:
(b - 2)(h + 4) = bh
Expanding the equation, we get:
bh + 4b - 2h - 8 = bh
Canceling the bh terms on both sides, we get:
4b - 2h - 8 = 0
Substituting the value of h from the first equation, we get:
4b - 2((5/3)b) - 8 = 0
Simplifying the equation, we get:
4b - (10/3)b - 8 = 0
(12/3)b - (10/3)b - 8 = 0
(2/3)b - 8 = 0
(2/3)b = 8
b = (3/2) * 8
b = 12 cm
Substituting the value of b in the first equation, we get:
h = (5/3) * 12
h = 20 cm
Therefore, the base of the triangle is 12 cm and the altitude is 20 cm, which matches with option 'D'.
Given that the altitude is five-thirds the length of the base, we can write the equation as:
h = (5/3)b
Since the area of a triangle is given by the formula: area = (1/2) * base * altitude, we can write the equation as:
(1/2) * b * h = area
Since the area remains the same, even after the changes in altitude and base, we can write the equation as:
(1/2) * (b - 2) * (h + 4) = (1/2) * b * h
Simplifying the equation, we get:
(b - 2)(h + 4) = bh
Expanding the equation, we get:
bh + 4b - 2h - 8 = bh
Canceling the bh terms on both sides, we get:
4b - 2h - 8 = 0
Substituting the value of h from the first equation, we get:
4b - 2((5/3)b) - 8 = 0
Simplifying the equation, we get:
4b - (10/3)b - 8 = 0
(12/3)b - (10/3)b - 8 = 0
(2/3)b - 8 = 0
(2/3)b = 8
b = (3/2) * 8
b = 12 cm
Substituting the value of b in the first equation, we get:
h = (5/3) * 12
h = 20 cm
Therefore, the base of the triangle is 12 cm and the altitude is 20 cm, which matches with option 'D'.
Community Answer
An altitude of a triangle is five-thirds the length of its correspondi...
12 cm and 20 cm
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An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, but the area of triangle remains the same. Find the base and altitude of the triangle respectively.a)100 cm, 24 cmb)24 cm, 10 cmc)20 cm, 12 cmd)12 cm, 20 cmCorrect answer is option 'D'. Can you explain this answer?
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An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, but the area of triangle remains the same. Find the base and altitude of the triangle respectively.a)100 cm, 24 cmb)24 cm, 10 cmc)20 cm, 12 cmd)12 cm, 20 cmCorrect answer is option 'D'. Can you explain this answer? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, but the area of triangle remains the same. Find the base and altitude of the triangle respectively.a)100 cm, 24 cmb)24 cm, 10 cmc)20 cm, 12 cmd)12 cm, 20 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, but the area of triangle remains the same. Find the base and altitude of the triangle respectively.a)100 cm, 24 cmb)24 cm, 10 cmc)20 cm, 12 cmd)12 cm, 20 cmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude is increased by 4 cm and the base is decreased by 2 cm, but the area of triangle remains the same. Find the base and altitude of the triangle respectively.a)100 cm, 24 cmb)24 cm, 10 cmc)20 cm, 12 cmd)12 cm, 20 cmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 8.
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