The diagonals of a rhombus have lengths 18 and 24. Find the length of one side. HELP!!?

Question

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Answer 1

Diagonals of a rhombus bisect each other at rightangles, so each side is the hypotenuse of a rightangled triangle with sides 9, 12.

Hypotenuse = 15

Answer 2

The diagonals of a rhombus are perpendicular, so if you take half of each diagonal you get the two smaller sides of a right-angled triangle with the side of the rhombus being the hypotenuse.
So the side length is √(9^12 + 12^2) = 15.

(Note that this is a 3, 4, 5 triangle, so you don't actually need to work out the square root.)

Answer 3

We know that the diagonals of a rhombus are perpendicular bisectors of each other, so imagining that the diagonals separate the rhombus into 4 equal RIGHT triangles, with the side being the hypotenuse and the legs are the halves of the diagonals, then,
s² = (18/2)² + (24/2)²
s² = 9² + 12²

Therefore,
s = 15

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If you need letters, then
Let ABCD be the rhombus, and let AC = 18 and BD = 24.

Also let the intersection of AC and BD be E.

Now AB = BC = CD = DA = s.

Since the diagonals of a rhombus are perpendicular bisectors of each other, then angle AEB is a right angle, and AE = 1/2 AC = 9 and EB = 1/2 BD = 12.

Therefore, ∆AEB is a right triangle.

Thus,
AB² = AE² + EB²

We substitute: AB = s, AE = 9 and EB = 12.
s² = 9² + 12²

Therefore,
s = 15
^_^

Answer 4

Since the diagonals of a rhombus are perpendicular bisectors they divide the rhombus into 4 congruent triangles. In each case, the two legs are half of each diagonal and the hypotenuse is one side.

Let

x = length of side of rhombus.

Applying the Pythagorean Theorem we have:

x² = (18/2)² + (24/2)² = 9² + 12² = 81 + 144 =225
x = 15

Answer 5

15

Answer 6

diagonals of a rhombus bisect each other at 90 degrees. thus side of the rhombus can be given by

s= sq. root ((d1/2)^2 + (d2/2)^2)

here, d1/2= 9
d2/2=12

thus s= sq. root ( 81+ 144) = sq. root ( 225) = 15