an equalateral triangle which is 48cm inside a square, how big is the square?

Answer 1

The square must be 48 cm but the triangle will only touch the square on one face / two corners.

Answer 2

If the side of the equilateral triangle is 48cm, then its vertical height, h, is:

Using Pythagoras Theorem,
h^2 + 24^2 = 48^2
h = 41.57cm

Since the height is shorter than the base, the sides of the square should be at least 48cm so as to fit the entire triangle.

The dimensions of the square has to be at least 48cm by 48cm.

Answer 3

The smallest square it can fit into is one with sides of 46.36 cm. The triangle is oriented so that one corner is touching one corner of the square and the other 2 corners are touching sides of the square. You basically cut the square into 4 triangles: the original equilateral triangle, two right triangles with 15 degree and 75 degree angles with a 48 cm hypotenuse and one right triangle with 45 degree and 45 degree angles and a 48 cm hypotenuse. To find the length of the sides of the square use the following:

cos(15) = side/48
side = 48cos(15)
side = 46.36 cm

Answer 4

Insufficient information. The square could be a mile wide. Very little information about the relationship of the triangle to the square.

Answer 5

48cm would be the logical answer.

But a 48cm equalateral triangle will fit into any square size bigger than 48cm.

Answer 6

let s=side of square

the smallest value of s which
will allow a 48cm equalateral
triangle to fit inside
=48(sqrt2+sqrt6)/4
=12(sqrt2+sqrt6)
=46.36443966cm
therefore,the square is
46.36443966cm x46.36443966cm

i hope that this helps

http://www.stetson.edu/~efriedma/triinsqu/

Answer 7

The square can be any size you want it to be as long as its side is >48cm

Answer 8

A sq., because of the fact it quite is in basic terms about as good as a triangle yet greater accommodating. Then, returned, a triangle is fascinating because of the fact it quite is greater suggestive of action, aspiration, and so on. yet i will follow the sq., rather now i'm previous and grey. (Gosh I do merchandise to those American spelling corrections! Which probable shows how sq. i'm)

Answer 9

I am guessing a little but this looks right !!!

if the equilateral triangle rests on the base of the square

use a(sq) + b(sq) = c(sq)

say the height of the triangle is h

we know that 1/2x X h = 48 cm(sq) (i) or h = 96/x

and h(sq) + 1/2x(sq) = x(sq) if u cut the triangle in half

thus h(sq) + 1/4x(sq) = x(sq) by pythagorus

substitute h = 96/x from (i)

but we know that x(sq) is the area of the square which we want

so h(sq) which is (96/x)squared + 1/4x(sq) = x(sq)

therefore (96/x)(sq) = 3/4x(sq)

so (96)(sq) = 3/4 x(4th) i.e x to the 4th power

and 9216 x 4 = 3 X x(4th)

then 36864 divided by 3 = x(4th)

so 12288 = x(4th)

root of x(4th) is x(sq)

therefore sq root of 12288 = x(sq) what u want !

area of the square = 110.85 cm(sq)

looks real messy but if u clean up with sq and 4th powers it works and looks right.

unless it was another sort of triangle in which case don't tell me cos i would have wasted my life !!!!

Answer 10

each side of it is 33.9cm
hypotenuse square is 2304 divide that by 2 because it is a square =1152 the square route of this is 33.941125 so that is your answer