Make a square from 20 right angled tri-angles?

Question

We have 20 right angled tri-angles with the opposite being 3cm and the adjacent being 6cm. What we need to do is make a square out of these. Making a 12cm by 15cm rectangle is easy, but we can't figure out how to make an accurate square. If you work the area out, the area of the square should be 180cm² .

Answer 1

I've worked out how it can be done. Lets see if I can explain how.
1 - make a rectangle out of 2 pieces, so that the long side is horizontal.
2 - repeat 3 more times, forming a column of 4 of these ractangles. (Pieces used = 8)
3 - against the sides of the middle two rectangles, place a vertical rectangle on either side (pieces used = 12). You should now have a fat cross shape.
4 - Place a triangle on the top of the column (so that the lengths match), and another on the right hand lower vertical rectangle (in the same direction. The point will stick out over the top of the vertical rectangle. The two sloping sides should form one long, continuous side).
5 - Repeat this on the other sides.
6 - You should then have a square (one that appears lopsided).
I hope you can understand this!

Answer 2

Perimeter = (x) + (3x) + (3x + 2) = 37 (given) ie 7x + 2 = 37 ie x = 5 Hence sides are 5, 15 and 17 units. Let the base = x ( to be calculated ) As per the given condition Area = x + 16 Height = 6 Now Area of the triangle = base x half of the height. = x . (6/2) = 3x But Area is also equal to ( x + 16 ) Hence 3x = x + 16 ie 2x = 16 ie x = 8 units Hence Length of the base x = 8 units. Perimeter of the triangle = 3 x 16 = 48 m Perimeter of the square = 4.x where x is the measurement of each side of the square. Hence 4x = 48 m ie x = 12m ............... Answer Let the width of the rectangle = x ft Hence its length = 2x ft. It is given the perimeter = 60 ft ie 2 ( 2x + x ) = 60 ft ie 6x= 60 ie x = 10 ft Now area of the rectangle = length x breadth = x.2x = 2.sq. of x = 2 ( Sq. of 10 ) = 200 sq.ft In this case the side of the isosceles triangle can have any whole number from 3 to 75. The original Dimensions are 9.6" x 38.4" ...... Answer If x is the measure of each of the equal angles Then the third angle = 2x - 36 But sum of these angles = 180 ie 2x + 2x - 26 = 180 ie x = 54 degree Therefore angles are 54 deg, 54 deg, and 72 deg .................... Answer

Answer 3

I don't really understand the shape of your triangles, but have you considered assembling them in pairs, to make ten rectangles, and then assembing those to form the borders of a hollow square, like a picture frame, with two fat edges on two opposite sides, and two thin edges along the other two opposite sides? You might be able to achieve an square outside edge, though the hole in the middle would not be square.

Answer 4

"opposite being 3cm and the adjacent being 6cm???"
what do u mean the opp. of the right angle is 3cm because that would be the hyp and there is adj 6cm side and it is not possible to have a larger side than the hyp.
Sry i didn't understand the question

Answer 5

for everyone who has forgotten gcse maths

http://www.content.org.uk/en/History_of_physics/80.html?title=Trigonometric_function#Right_triangle_definitions


heres a clue for you

the area of a square is length x length.

the square root of your resultant square is 13.7, which is equal to two hypoteneuse for your right angled triangles...... which means that your square should be two hypoteneuse in length and two hypoteneuse in height

Answer 6

you cant. not if the triangles are all whole number sides then u cant make a square. 180 doesnt hav a whole square root. sorry mate. if i were u id giv in.
its not physically poissible without cutting up ur triangles.

Answer 7

WHY.?