CAT 2018

Slot 1

QA

Question & Solution

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?

We know that AC is the diameter and $\angle$ ABC = 90°. AC = 2*13 = 26 cm

In right angle triangle ABC,

$AC^2 = AB^2 + BC^2$

$\Rightarrow$ $AB^2+BC^2=26^2$

$\Rightarrow$ $AB^2+BC^2=676$

Let us check with the options.

Option (A): $24^2+10^2 = 676$. Hence, this is a possible answer. 

Option (B): $25^2+9^2 = 706  eq 676$.  Hence, this is an incorrect pair.

Option (C): $25^2+10^2 = 725 eq 676$.  Hence, this is an incorrect pair.

Option (D): $24^2+12^2 = 720 eq 676$. Hence, this is an incorrect pair.

Therefore, we can say that option A is the correct answer.