ABCD is a square of side 10 units. P, Q, R and S are midpoints of sides AD, DC, CB and BA respectively. Find the length of JK?
Explanation:
In ASCQ, AS = QC and also AS || QC ⇒ ASCQ is a parallelogram.
Since the figure is symmetric we get AJ = DM = CL = BK, and PJ = QM = RL = SK, and JM = ML = LK = KJ
Now, in ∆DCL, DQ = QC and QM || CL ⇒ DM = ML (By Basic Proportionality Theorem) and also, MQ = ½ LC
Let LC = 2x ⇒ QM = x
∴ DR = DM + ML + LR = 2x + 2x + x = 5x
In right triangle DCR, DR2 = DC2 + CR2
⇒ (5x)2 = 102 + 52
⇒ 25x2 = 125
⇒ x2 = 5
⇒ x = √5
∴ JK = 2x = 2√5
Hence, option (b).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.