Question
Quantitative Aptitude Question on Mensuration
Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
A
24,10
B
25,9
C
24,12
D
25,10
Answer
24,10
Explanation
Solution
The correct answer is (A):
We know that AC is the diameter and ∠ ABC = 90°. AC = 2*13 = 26 cm
In right angle triangle ABC,
AC2 = AB2 + BC2
⇒ AB2 + BC2 = 262
⇒ AB2 + BC2 = 676
Let us check with the options.
Option (A): 242 + 102 = 676
Option (B): 252 + 92 = 706 ≠ 676
Option (C): 252 + 102 = 725 ≠ 676
Option (D): 242 + 122 = 720 ≠ 676.