Answer:
See the attached figure which represents the problem.
As shown, AA₁ and BB₁ are the altitudes in acute △ABC.
△AA₁C is a right triangle at A₁
So, Cos x = adjacent/hypotenuse = A₁C/AC ⇒(1)
△BB₁C is a right triangle at B₁
So, Cos x = adjacent/hypotenuse = B₁C/BC ⇒(2)
From (1) and (2)
∴ A₁C/AC = B₁C/BC
using scissors method
∴ A₁C · BC = B₁C · AC
Lets do
Write in standard form
Given:
The area of the squares are given.
To find:
The exact side length or estimate side length of the square.
Solution:
We know that, the area of a square is
Where, a is the side length of the square.
Area of the square is 100 square units. So, the side length is:
Therefore, the side length is 10 units.
Area of the square is 95 square units. So, the side length is:
It is not exact. We know that .
Therefore, the side length is between 9 and 10.
Area of the square is 36 square units. So, the side length is:
Therefore, the side length is 6 units.
Area of the square is 30 square units. So, the side length is:
It is not exact. We know that .
Therefore, the side length is between 5 and 6.