A question has been received in the image form as below:
While it can be solved by many methods; perhaps it will be better to solve it considering that this triangle is similar to the Egyptian Triangle ( 3-4-5 Right Triangle).
There is a property of 3-4-5 right triangles that the inner sides of the square inscribed in it divide the sides of the triangle in the ratio of 3:4.
As the hypotenuse of the problem figure is divided in the ratio of 3:4, clearly this is a scaled up triangle similar to the 3-4-5 right triangle.
The Hypotenuse is 84/5 times of the original hypotenuse of the Egyptian triangle. So now we can write the base equal to 4*84/5= 336/5 and perpendicular equal to 252/5.
The upper portion of the perpedicular will be 3/7 of 252/5 and the lower portion will be 4/7 of 252/5.
The left portion of the base will be 3/7 of 336/5 and the right portion will be 4/7 of 336/5.
The whole problem is now reduced to simple calculation as shown in the hand written note produced below:
The whole idea is why to reinvent the wheel! It is existing beautifully for us. We have to make vehicles only to surge ahead.
When we know about the Egyptian Triangle, it is better to apply its properties to such problems.
You may wish to click here to go through the blog post on Egyptian Triangle once again and make your own notes or formulae for such problems.
