Question

The roof of a building is 8 m high. A rope is
tied from the roof to a peg on the ground
6 m away from the wall. What would the
minimum length of the rope?​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given building 8m high
• A rope is tight to a peg on ground, 6m away from the building

To Find:

• We have to find the length of Rope

Concept Used:

On Analyzing the Question

A Right angle triangle will be formed which can be solved further by using Pythagoras Theorm

$\large\underline{\orange{\sf{Pythagoras \: Theorm }}}$

In Right Angle Triangle, the square of Hypotenuse is equal to the sum of square of other two sides

$\boxed{\sf{Hypotenuse^2 = Perpendicular^2 + Base^2}}$

$\sf{ }$

Solution:

Let us assume

• AB = Height of Building
• BC = Distance of peg from Building
• AC = Length of Rope

We have been given that

$\boxed{\sf{AB = 8 \: m}}$

$\boxed{\sf{BC = 6 \: m}}$

$\sf{ }$

$\odot \:$Using Pythagoras Theorm

In ∆ABC Using Pythagoras Theorm

$\implies \sf{(AC)^2 =(AB)^2 +(BC)^2}$

Substituting the Values

$\implies \sf{(AC)^2 =(8)^2 +(6)^2}$

$\implies \sf{(AC)^2 =64 +36}$

$\implies \sf{(AC)^2 =100}$

Taking Square Root on Both sides

$\implies \sf{AC = \sqrt{100}}$

$\implies \boxed{\sf{AC = 10 m }}$

Length of Rope needed is 10m

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$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Length \: of \: Rope = 10 \: m}}$

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