solution :-
let the ladder BC reaches the building at c
let the height of building where the ladder reaches be ac
now according to question :-
BC = 25mAC = 24m
now we need to find the distance of the root of the ladder from the building
as we know that it is right angled triangle so we can apply Pythagoras theorem
\begin{gathered}:\implies\sf \: bc^{2} = ab^{2} + ac^{2} \\ \end{gathered}:⟹bc2=ab2+ac2
here bc² is the hypotenuse side
and two right angle sides are ab,AC
now,
\begin{gathered}:\implies\sf \: ab^{2} = bc^{2} - ac^{2} \\ \end{gathered}:⟹ab2=bc2−ac2
by putting values we get,
\begin{gathered}:\implies\sf \: ab^{2} = {25}^{2} - {24}^{2} \\ \end{gathered}:⟹ab2=252−242
by squaring these values we get,
\begin{gathered}:\implies\sf \: ab^{2} = 625 - 576 \\ \end{gathered}:⟹ab2=625−576
now by subtracting 625 - 576 we get,
\begin{gathered}:\implies\sf \: ab^{2} = 49 \\ \end{gathered}:⟹ab2=49
take the square to opposite side it will become square root to the number
\begin{gathered}:\implies\sf \: ab \: = \sqrt{49} \\ \end{gathered}:⟹ab=49
we can write 49 as 7 × 7
\begin{gathered}:\implies\sf \: ab \: = \sqrt{7 \times 7} \\ \end{gathered}:⟹ab=7×7
now by taking the number out from the square root we can take one number so we get
\begin{gathered}:\implies\sf \: ab \: = 7m \\ \end{gathered}:⟹ab=7m
so therefore the distance of foot of the ladder from the building is 7m
Note :-
this method can apply to equilateral triangle and isoceles right triangle also if two straight lines are given.
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