what would the answer be?
2006-06-20 03:22:28 · 15 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
6√2
Remember it's a square so the sides are all the same length, and the area is s^2
so s^2=36==>s^2-36=(s-6)(s+6)=0 so s is either 6 or -6. -6 makes no sense here, so it is obviously 6.
Now, since we have a square we can "draw" (imagine) a line at the diagonal, and that makes a right triangle (since the corners of a square are all 90º) with legs 6 and 6. using the Pythagorean relation, we have d^2=s^2+s^2=6^2+6^2=72. Thus d^2-72=(d-6√2)(d+6√2)=0. Thus d is either 6√2 or -6√2, and again is obviously the positive one :)
2006-06-20 03:26:16 · answer #1 · answered by Eulercrosser 4 · 0⤊ 0⤋
Since the area is 36, one side of the square is 6. Now use the Pythagorean Theorem to find length of the diagonal:
6^2 + 6^2 = c^2
72 = c^2
c= √72 = 6√2
2006-06-20 06:48:13 · answer #2 · answered by menezes_dean 2 · 0⤊ 0⤋
A = L x B
A = L^2 (square)
L=6
Using A^2 +B^2 = Diagonal^2
so sqrt( 36 + 36) = Diagonal
so diagonal is 8.485
2006-06-20 03:27:53 · answer #3 · answered by CRAZYDEADMOTH 3 · 0⤊ 0⤋
A square of area 36 has sides of length sqrt(36) = 6
The diagonal is the square root of 2 times the length of the side
D = sqrt(2)*6 = 8.4852813742385713....
2006-06-20 03:27:18 · answer #4 · answered by poorcocoboiboi 6 · 0⤊ 0⤋
Since the diagonal will make a triangle within the square you can use the equation a^2 + b^2 = c^2 Where (a) and (b) are the known side lengths. You will get the same answer as above (8.485...).
2006-06-20 03:30:58 · answer #5 · answered by ebk1974 3 · 0⤊ 0⤋
Using Pythagorean Theorem, we know the legs to be 6 units long. 6^2 + 6^2 =72. Take the square root, you are going to get 8 sq. root of 3 for your diagonal.
2006-06-20 03:27:49 · answer #6 · answered by Anonymous · 0⤊ 0⤋
The square root of 36 is 6, so you have a square there with a side length of 6.
Just apply rules of basic 45-45-90 triangles and multiply your side length by the square root of 2.
You get 6sqrt(2).
2006-06-20 03:27:52 · answer #7 · answered by Anonymous · 0⤊ 0⤋
Area = 36
Area = side^2
so side length is 6.
By the pythagorean theorem
diagonal^2 = 6^2 + 6^2
diagonal^2 = 72
diagonal = 6 * root(2)
2006-06-20 03:27:11 · answer #8 · answered by fatal_flaw_death 3 · 0⤊ 0⤋
Formulae:
A = s²
d = s√2
in the 1st equation solve for s
s² = A
s = √A
Subs. into the 2nd equation
d = √A√2
d = √(2A)
Given A = 36
d = √(2 · 36)
d = 6√2
^_^
2006-06-21 00:33:48 · answer #9 · answered by kevin! 5 · 0⤊ 0⤋
Area = a^2
a^2 = 36
a = 6
a^2 + a^2 = c^2
2a^2 = c^2
2(6)^2 = c^2
2 * 36 = c^2
c = sqrt(2 * 36)
c = 6sqrt(2)
ANS : 6sqrt(2)
2006-06-20 03:32:00 · answer #10 · answered by Sherman81 6 · 0⤊ 0⤋