Question

pls solve this my examm fast guys i beg u all​

Answer 1

$\LARGE\textbf{\underline{\underline{Given :-}}}$

• In first condition :-

➙ The top of the ramp is above the ground level at the height of 7.5 m .

➙ The distance between the ramp and the wall is of 10 m .

• In second condition :-

➙ The ramp is placed on the opposite wall and its top is above the ground level at a height of 10 m .

$\LARGE\textbf{\underline{\underline{To find :-}}}$

• In first condition :-

➙The length of the ramp = ?

• In second condition :-

➙ The distance between the ramp and the wall = ?

$\LARGE\textbf{\underline{\underline{Formula :-}}}$

• Here we have to use the Pythagoras Theorem . Because, we know that general the angle between the wall and ground is of 90° .

• So by using the Pythagoras Theorem in the first condition we can find the length of the ramp . And when we would get the length of the ramp we can find the distance between the ramp and the wall in the second condition .

• Pythagoras Theorem :-

$\boxed{\leadsto\large\textbf{ Hypotenuse^{2} = base^{2} + height^{2} }}$

$\LARGE\textbf{\underline{\underline{Here :-}}}$

• Hypotenuse = Length of the ramp.
• Base = Distance between the ramp and the wall.
• Height = The top of the wall where the ramp touches.

$\LARGE\textbf{\underline{\underline{Solution :-}}}$

• In first condition :-

1. Base = 10 m
2. Height = 7.5 m
3. Hypotenuse = ? .........( length of the ramp )

• Using Pythagoras Theorem :-

$\therefore\large\textsf{ Hypotenuse^{2} = 10^{2} + 7.5^{2} }$

$\therefore\large\textsf{ Hypotenuse^{2} = 100 + 56.25 }$

$\therefore\large\textsf{ Hypotenuse^{2} = 156.25 }$

$\therefore\large\textsf{Hypotenuse = \sqrt[2]{156.25} }$

$\therefore\large\textsf{Hypotenuse = 12.5 m}$

$\boxed{\therefore\large\textbf{Length of the ramp = 12.5 m}}$

• In second condition :-

➙ As we have got the length of the ramp so we can assume it as the hypotenuse .

1. Base = ?........ ( distance between the ramp and the wall )
2. Height = 10 m
3. Hypotenuse = 12.5 m

• Using Pythagoras Theorem :-

$\therefore\large\textsf{ Hypotenuse^{2} = base^{2} + height^{2} }$

$\therefore\large\textsf{ 12.5^{2} = base^{2} + 10^{2} }$

$\therefore\large\textsf{ 156.25 = base^{2} + 100 }$

$\therefore\large\textsf{ 156.25 - 100 = base^{2} }$

$\therefore\large\textsf{ 56.25 = base^{2} }$

$\therefore\large\textsf{ \sqrt[2]{56.25}= base }$

$\boxed{\therefore\large\textbf{7.5 = base}}$

• Therefore the distance between the ramp and the wall is 7.5 m.

$\LARGE\textbf{\underline{\underline{*Note :-}}}$

Instead of writing base , hight and hypotenuse in the paper.

Write :-

• In first condition :-

1. Base = BO
2. Height = AB
3. Hypotenuse = BO

• In second condition :-

• Base = OC
• Height = DC
• Hypotenuse = DO

* This is according to the markings in the figure.