Question

A pair of ladders whose lengths are 4.2 M and 5.6 M are leaned onto a wall such that they reach the same height. The base of the longer ladder is 1.96 M further away from the base of the wall then the base of the shorter ladder. The distance of the shorter ladder form the wall is

Answer 1

Answer:

2.54 meters is answer please add me as Brainiest

Step-by-step explanation:

Solution−

↝ Let height of the wall, AB = 'h' meter.

↝ Let foot of the shorter ladder be at point C and foot of the longer ladder be at point D from the base B.

Let the shorter ladder of length 4.2 m is 'x' meter away from the base of the wall.

↝ Therefore, BC = 'x'

So, the foot of the longer ladder of length 5.6 m is 'x + 1.95' meter away from the base of the wall.

↝ Therefore, BD = 'x + 1.95'

Now,

↝ In ∆ ABC

By pythagoras theorem,

⇛ AC² = AB² + BC²

⇛ (4.2)² = h² + x²

⇛ 17.64 = h² + x² --------(1)

↝ Aɢᴀɪɴ,

↝ In ∆ ABD,

By Pythagoras theorem,

⇛ AD² = AB² + BD²

⇛ (5.6)² = h² + (x + 1.95)²

⇛ 31.36 = h² + x² + 3.8025 + 3.9x

\boxed{\sf \: \because \: {(x +y)}^{2} = {x}^{2} + {y}^{2} + 2xy}

∵(x+y)

2

=x

2

+y

2

+2xy

⇛ 31.36 = 17.64 + 3.8025 + 3.9 x [using (1)]

⇛ 31.36 - 17.64 - 3.8025 = 3.9 x

⇛ 9.9175 = 3.9 x

⇛ x = 2. 54 meter approximately.

Additional Information :-

1. Pythagoras Theorem :-

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

2. Converse of Pythagoras Theorem :-

'' If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle''.

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Answer 2

Given,

A pair of ladders whose lengths are $4.2m$ and $5.6m$ are leaned onto a wall such that they reach the same height. the base of the longer ladder is $1.96m$ further away from the base of the wall then the base of the shorter ladder.

Formula,

$hypotenuse^{2} =height^{2}+base^{2}$

Let '$h$' be height of the both ladders and  '$x$' be the base of the shorter ladder.

First apply the Pythagoras theorem to the longer distance

$5.6^{2}=h^{2}+(1.96+x)^{2}$

$31.36=h^{2}+x^{2} +1.96^{2}+3.92x\\31.36=h^{2}+x^{2} +3.8416+3.92x$

$h^{2}+x^{2} =27.5184-3.92x$_____(1)

Let apply Pythagoras theorem to shorter distance

$4.2^{2}=x^{2} +h^{2}$

$17.64=x^{2} +h^{2}$_____(2)

Substitute equation(1) in equation (2)

$17.64=27.5184-3.92x\\3.92x=27.5184-17.64\\3.92x=9.87\\x=2.52$

Therefore, the distance of the shorter ladder from the wall is $2.52m$.