Question

There is a deep river in a village. The villagers want to measure its breadth without crossing the river as force of current of river- water is very strong. Ramesh a student of class VII of that village came and said "I will measure the breadth of the river without crossing it." He came on the bank of the river at a point A and imagined a point B just opposite on the other bank. He moves to C and then D such that C is equidistant from A and D. Then he moves to E such that B, C and E are on the same line and DE is perpendicular to the bank of the river.

Answer 1

Answer:

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Step-by-step explanation:

Consider AB as the breadth of the river. Take a point M at a distance from B. Draw a perpendicular from the point M and name it as N so that it joins the point A as a straight line.

Now in △ABO and △NMO

We know that

∠OBA=∠OMN=90

∘

We know that O is the midpoint of the line BM

So we get

OB=OM

From the figure we know that ∠BAO and ∠MON are vertically opposite angles

∠BAO=∠MON

By ASA congruence criterion

△ABO≅△NMO

AB=NM(c.p.c.t)

Therefore, MN is the width of the river.