Question

Hello

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

Answer 1

Heya!!☻☻

Here's your answer!!
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Let AB be the breadth of the river. mark a point β on the bank of the river. move Along the river bank to a point Ο. then move along the river bank in the same direction to point ℳ such that
ΒΟ = OM

Now from ℳ move along the path MN perpendicular to the river bank BM to a point N such that A, O and N are in a straight line.

measure the length of MN. the length of MN will be required breadth of the river.

ᴘʀᴏᴏғ : AB perpendicular BM and MN perpendicular BM

In rt. ∠s ABO and NMO,

∠ABO = ∠NMO (EACH 90°)

BO = MO (const.)

∠AOB = ∠NOM (vert. opp. ∠s)

∴ ∆ABO = ∆NMO (AAS axiom)

∴ AB = MN
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Answer 2

$\color {blue} {Your~Solutions:---}$

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$\bold {Let~AB~be~the~breadth~of~the~river. }$

Mark a point 'B' on the bank of the river.
Move Along the river bank to a point 'Ο'.

$\textbf Now,$
Move along the river bank in the same direction to point 'M' such that,
ΒΟ = OM

From 'M' move along the path $\underline {MN}$ perpendicular to the river bank $\underline {BM}$to a point 'N' such that 'A', 'O' and 'N' are in a straight line.

Measure the length of $\underline {MN}$.
The length of $\underline{MN}$ will be required breadth of the river.

$\underline {\bold {PROOF:-}}$
$\underline{AB}$perpendicular $\underline{BM}$ and $\underline{MN}$ perpendicular $\underline{BM}$

$\bold {In~∠ABO~and~∠NMO,}$

$\bold {∠ABO = ∠NMO (Each~∠= 90°)}$

$\bold {BO = MO (by~construction)}$

$\bold {∠AOB = ∠NOM (V.O.A)}$

$\bold {∴ tri. ABO ≈ tri. NMO (AAS~axiom) }$

$\bold {∴ AB = MN}$

SO,
Breadth = $\underline{AB}$ = $\underline{MN}$





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$\bold {Hope~it~helps~you }$