Question

a 10m long ladder is placed against a wall .The foot of ladder is 6 m from the wall how far up the wall does the top of ladder reach ​

Answer 1

Answer:

The top of the ladder reach 8 m up on the wall

Explanation:

length of the ladder = 10 m

base of the ladder is 6m from the wall

as the wall makes an angle of 90° i.e right angle then

using the pythagoras theorem to find the length of the wall does the top of the ladder reach ​

here

hypotenuse = 10 m

base = 6 m

we need to find the perpendicular

then

h²= p² + b²

10²= p² + 6²

100 = p² + 36

100 - 36 = p²

64 = p²  

p = √64

p = 8 m  

hence ,

The top of the ladder reach 8 m up on the wall

Answer 2

GivEn:

• Length of ladder = 10 m
• Base of ladder from the wall = 6 m

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To find:

• How far up the wall does the top of ladder reach?

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Solution:

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We know that,

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• Wall makes an angle of 90°.

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$\underline{\bigstar\:\boldsymbol{Using\: Pythagoras\:Theorem\::}}$

$\setlength{\unitlength}{1.2cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf P}\put(4,2.5){\large\bf 10 m}\put(2.8,.3){\large\bf 6 m}\put(1.02,1.02){\framebox(0.3,0.3)}\end{picture}$

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$\sf Here \begin{cases} & \sf{Hypotenuse,\;H = \bf{10\;cm}} \\ & \sf{Base,\;B = \bf{6\;cm}} \end{cases}$

$\star\;{\boxed{\sf{\purple{(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2}}}}$

$\dag\;{\underline{\frak{Putting\;values\;:}}}$

$:\implies\sf (10)^2 = (6)^2 + (P)^2\\ \\ :\implies\sf 100 = 36 = P^2\\ \\ :\implies\sf P^2 = 100 - 36\\ \\ :\implies\sf P^2 = 64\\ \\ :\implies\sf P = \sqrt{64}\\ \\ :\implies{\boxed{\sf{\pink{P = 8\;cm}}}}\;\bigstar$

$\therefore$ Hence, the top of ladder reach 8 m up on the wall.