Question

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 1.95m 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:


option
a) 2,5meters
b) 2,51meters
C) 2,53m
d) 2,52m
​

Answer 1

$\large\underline{\sf{Solution-}}$

↝ 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

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

⇛ 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''.

Answer 2

Answer:

Step-by-step explanation:

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