ABCD is a square with each side measuring 144 cm. M is a point on CB such that CM=36 cm. If N is a variable point on the diagonal DB, find the least value of CN+MN.
Answer:
180 cm
- Given, BC=144 cm and CM=36 cm
⟹BM=CB−CM=144−36=108
Let's join A to N - Since △ADN≅△CDN[By SAS criterion]∴AN=CN[Corresponding sides of congruent triangles]
⟹ AN+MN=CN+NM
Observe that the value of AN+NM is least when ANM is a straight line. - Now, if ANM is a straight line, then △AMB is a right-angled triangle.
∴ by Pythagoras theorem,
From step 2, we have AN+MN=CN+NM.Least value of AN+NM =√AB2+BM2=√1442+1082=180 - Hence, the least value of CN+MN is 180 cm.