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In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, is
Correct answer is '2'. Can you explain this answer?
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In a right-angled triangle ABC, the altitude AB is 5 cm, and the base ...
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In a right-angled triangle ABC, the altitude AB is 5 cm, and the base ...
Given information:
- Altitude AB = 5 cm
- Base BC = 12 cm
- Areas of ΔABP, ΔABQ, and ΔABC are in arithmetic progression
- Area of ΔABC = 1.5 times the area of ΔABP
Solution:
Step 1: Find the area of ΔABC
Area of ΔABC = 0.5 * base * height
Area of ΔABC = 0.5 * 12 * 5
Area of ΔABC = 30 cm²
Step 2: Find the area of ΔABP
Given that the area of ΔABC is 1.5 times the area of ΔABP
Area of ΔABP = 30 / 1.5 = 20 cm²
Step 3: Find the area of ΔABQ
Since the areas of ΔABP, ΔABQ, and ΔABC are in arithmetic progression, let the area of ΔABQ be x
20, x, 30 are in arithmetic progression
x = 2 * 20 - 30
x = 10 cm²
Step 4: Find the length of PQ
Let the length of PQ be y cm
Area of ΔABP = 0.5 * AB * y
20 = 0.5 * 5 * y
y = 8 cm
Therefore, the length of PQ is 8 cm.
- Altitude AB = 5 cm
- Base BC = 12 cm
- Areas of ΔABP, ΔABQ, and ΔABC are in arithmetic progression
- Area of ΔABC = 1.5 times the area of ΔABP
Solution:
Step 1: Find the area of ΔABC
Area of ΔABC = 0.5 * base * height
Area of ΔABC = 0.5 * 12 * 5
Area of ΔABC = 30 cm²
Step 2: Find the area of ΔABP
Given that the area of ΔABC is 1.5 times the area of ΔABP
Area of ΔABP = 30 / 1.5 = 20 cm²
Step 3: Find the area of ΔABQ
Since the areas of ΔABP, ΔABQ, and ΔABC are in arithmetic progression, let the area of ΔABQ be x
20, x, 30 are in arithmetic progression
x = 2 * 20 - 30
x = 10 cm²
Step 4: Find the length of PQ
Let the length of PQ be y cm
Area of ΔABP = 0.5 * AB * y
20 = 0.5 * 5 * y
y = 8 cm
Therefore, the length of PQ is 8 cm.
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In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, isCorrect answer is '2'. Can you explain this answer?
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In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, isCorrect answer is '2'. 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 In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, isCorrect answer is '2'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, isCorrect answer is '2'. Can you explain this answer?.
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