Question

answer this question​

Answer 1

Question :-

a ladder 25m long just reaches the top of a building 24m high from the ground what is the distance between the foot of the ladder from the building ??

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 = 25m
• AC = 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

$:\implies\sf \: bc^{2} = ab^{2} + ac^{2}$

here bc² is the hypotenuse side

and two right angle sides are ab,AC

now,

$:\implies\sf \: ab^{2} = bc^{2} - ac^{2}$

by putting values we get,

$:\implies\sf \: ab^{2} = {25}^{2} - {24}^{2}$

by squaring these values we get,

$:\implies\sf \: ab^{2} = 625 - 576$

now by subtracting 625 - 576 we get,

$:\implies\sf \: ab^{2} = 49$

take the square to opposite side it will become square root to the number

$:\implies\sf \: ab \: = \sqrt{49}$

we can write 49 as 7 × 7

$:\implies\sf \: ab \: = \sqrt{7 \times 7}$

now by taking the number out from the square root we can take one number so we get

$:\implies\sf \: ab \: = 7m$

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.

Answer 2

Answer:

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 = 25m

AC = 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.