Problem Solving

Four 3-4-5 right triangles and a square whose sides are 5 are arranged to form a second square. What is the perimeter of that square?

tsmith93 wrote:Four 3-4-5 right triangles and a square whose sides are 5 are arranged to form a second square. What is the perimeter of that square?

Area of a 3-4-5 triangle =6

Total area of the four triangles = 24
Area of the square with side 5 = 25

Total area of the triangles are square combined = 49

And if that is a square side of the square = 7
Perimeter = 4*7=28

ajith wrote:

tsmith93 wrote:Four 3-4-5 right triangles and a square whose sides are 5 are arranged to form a second square. What is the perimeter of that square?

Area of a 3-4-5 triangle =6

Total area of the four triangles = 24
Area of the square with side 5 = 25

Total area of the triangles are square combined = 49

And if that is a square side of the square = 7
Perimeter = 4*7=28

I am curious to see the square so made.

The square with the side 5 will be in the middle.
that way it will correspond to the hypotenuse of the 3 4 5 sqare.
place the 3 4 5 squares on each side of the square with side 5
How ?
Let the sqaure be A B C D and the 3 4 5 triangle be X Y Z with YZ = 5 and X = 90°
place Y Z on AB such that Z corresponds to A and Y to B
the next X² Y² Z² will be placed on side BC such that
now Z² corresponds to B and Y² corresponds to C
the line X B X² is 7 unit
continue in this fashion. Each side of the square will be 7 units.

kstv wrote:The square with the side 5 will be in the middle.
that way it will correspond to the hypotenuse of the 3 4 5 sqare.
place the 3 4 5 squares on each side of the square with side 5
How ?
Let the sqaure be A B C D and the 3 4 5 triangle be X Y Z with YZ = 5 and X = 90°
place Y Z on AB such that Z corresponds to A and Y to B
the next X² Y² Z² will be placed on side BC such that
now Z² corresponds to B and Y² corresponds to C
the line X B X² is 7 unit
continue in this fashion. Each side of the square will be 7 units.

I am still crying for a feature on BTG that could enable us to show what is running in mind by some drawing.

Second sanju09 and want to add
that the readability can be improved if there was a method to represent the math symbols like √ x² 90° without having to remember the ASCII code
for example (x^2) + y ^3 * sq rt 8
is much better as x² √8
In the same fashion we add emotions it is possible to list out the common symbols.
Technique is being used by Regional language site who do't use Latin Alphabets.
If BTB accede to the request it'll be great.
Please ignore the diagonal of the sq I know why it is there but cannot get it out.

kstv wrote:Second sanju09 and want to add
that the readability can be improved if there was a method to represent the math symbols like √ x² 90° without having to remember the ASCII code
for example (x^2) + y ^3 * sq rt 8
is much better as x² √8
In the same fashion we add emotions it is possible to list out the common symbols.
Technique is being used by Regional language site who do't use Latin Alphabets.
If BTB accede to the request it'll be great.
Please ignore the diagonal of the sq I know why it is there but cannot get it out.

now kewl...only if wish is answered