Let ABC be a right-angled triangle | Quantitative Aptitude Questions - CAT Geometry
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The question below is from previous year CAT question from CAT 2019 exam comes from sub-section Geometry: Let ABC be a right-angled triangle. Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:
CAT 2019 – Slot -2-Quantitative Aptitude- Question 2 - Let ABC be a right-angled triangle
Q. 2: Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is
1. 10
2. 8√2
3. 6√2
4. 5
Let AB = a and AC = b
A^2 + b^2 = 400 by pythagoras
Let AP = x and BP = y, so CP= 20-y
So, by Pythagoras
X^2 + y^2 = a^2 and b^2 = x^2 + (20-y)^2
Maximum possible value of AP occurs when a = b, so a= b=10 root 2
On solving, we get AP = 10 units
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