Question

In the adjoining figure, explain how one can find the breadth of the river without crossing it.

Answer 1

Let AB be the breadth of the river.

M is any point situated on the bank of the river.

Let O be the mid point of BM.

Moving along perpendicular to point such that A,O and N are in a straight line.

Then MN is the required breadth of the river.

In △OBA and △OMN, we have:OB=OM

∴△OBA≅△OMN (ASA criterion)

(O is midpoint)∠OBA=∠OMN

(Each 90°)∠AOB=∠NOM

(Vertically opposite angle)

Thus, MN = AB (CPCT)

If MN is known, one can measure the width of the river without actually crossing it.