the diagonals of a rhombus have lengths 4 and 12. what is the length of a side in simplest form.
a=sqroot(12^2+4^2)
a=sqroot(144+16)
a=sqroot(160)
a=sqroot(16*10)
a=4*sqroot(10)=12.64911
Becouse sqroot(16)=4
a=4*sqroot(10)=12.64911
That is the wrong answer.
p=first diagonal=4
q=second diagonal=12
a=sqroot[(p/2)^2+(q/2)^2]
a=sqroot[(4/2)^2+(12/2)^2]
a=sqroot(2^2+6^2)
a=sqroot(4+36)
a=sqroot(40)
a=sqroot(4*10)
a=2*sqroot(10)
OR:
p^2+q^2=4a^2 Divide with 4
a^2=(p^2+q^2)/4
a=sqroot[(p^2+q^2)/4]
a=sqroot(p^2+q^2)/sqroot(4)
a=sqroot(p^2+q^2)/2
a=sqroot(4^2+12^2)/2
a=sqroot(16+144)/2
a=sqroot(160)/2
a=sqroot(16*10)/2
a=4*sqroot(10)/2
a=2*sqroot(10)
Check this.
In google type:
mathworld.wolfram rhombus
When page be open click on :
Rhombus-from Wolfram MathWorld
Why did the rhombus go to the doctor?
Because it was feeling a little "off-"sides!
Now, let's solve this riddle of sides together.
In a rhombus, the diagonals bisect each other at right angles. So, we can form two right triangles by connecting the midpoint of one diagonal to the vertices of the rhombus.
Since the lengths of the diagonals are 4 and 12, the lengths of the diagonals' midlines (or half of the rhombus's sides) are 2 and 6, respectively.
Using the Pythagorean theorem, we can find the lengths of the sides of those right triangles:
1. In the first right triangle, the shorter side is 2 and the longer side is the length of one side of the rhombus. So, we have:
(2)^2 + (side)^2 = (12/2)^2
4 + (side)^2 = 36
(side)^2 = 36 - 4
(side)^2 = 32
2. In the second right triangle, the shorter side is 6 and the longer side is also the length of one side of the rhombus. So, we have:
(6)^2 + (side)^2 = (4/2)^2
36 + (side)^2 = 16
(side)^2 = 16 - 36
(side)^2 = -20
Uh-oh! It seems we hit a snag in our calculations. A negative value suggests an error, indicating that the given lengths of 4 and 12 for the diagonals may not be correct.
So, the length of a side of the rhombus cannot be determined with the information provided. But hey, at least we had fun along the way, right?
To find the length of a side of a rhombus, you can use the Pythagorean Theorem. In a rhombus, the diagonals are perpendicular bisectors of each other, meaning they split the rhombus into four congruent right triangles.
Let's call the length of one side of the rhombus "s". The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, one of the right triangles can be formed using the half of one diagonal (which is 4/2 = 2) and one side of the rhombus (which is "s/2" since it is half of the side). Using the Pythagorean theorem, we have:
(2)^2 + (s/2)^2 = (12/2)^2
Simplifying the equation, we have:
4 + (s^2)/4 = 36
Multiplying the entire equation by 4 to eliminate the fraction, we get:
16 + s^2 = 144
Rearranging the equation, we have:
s^2 = 144 - 16
s^2 = 128
To find the length of a side in simplest form, we take the square root of both sides:
√(s^2) = √128
s = √128
To simplify the square root of 128, we can factor out the largest perfect square:
s = √(64 * 2)
s = 8√2
Therefore, the length of one side of the rhombus is 8√2.
To find the length of a side of a rhombus, we can use the Pythagorean theorem. The diagonal of a rhombus divides it into two congruent right triangles. Let's label the length of one of the diagonals as "d1" and the length of the other diagonal as "d2". In this case, we have d1 = 4 and d2 = 12.
Now, let's find the lengths of the sides of the rhombus.
Since the diagonals of a rhombus are perpendicular bisectors of each other, the diagonals divide the rhombus into four congruent right triangles. Let's label the sides of the rhombus as "s1" and "s2".
From the Pythagorean theorem, we know that the square of the diagonal's length is equal to the sum of the squares of the sides of the rhombus.
For one of the right triangles, we have:
(s1/2)^2 + (s2/2)^2 = (d1/2)^2
Substituting the values we have:
(s1/2)^2 + (s2/2)^2 = (4/2)^2
(s1/2)^2 + (s2/2)^2 = 2^2
(s1/2)^2 + (s2/2)^2 = 4
Similarly, for the other right triangle, we have:
(s1/2)^2 + (s2/2)^2 = (d2/2)^2
(s1/2)^2 + (s2/2)^2 = (12/2)^2
(s1/2)^2 + (s2/2)^2 = 6^2
(s1/2)^2 + (s2/2)^2 = 36
Now, let's solve the system of equations:
(s1/2)^2 + (s2/2)^2 = 4 --(1)
(s1/2)^2 + (s2/2)^2 = 36 --(2)
By subtracting equation (1) from equation (2), we get:
(s1/2)^2 + (s2/2)^2 - (s1/2)^2 - (s2/2)^2 = 36 - 4
0 = 32
This means that the system of equations is inconsistent, which implies that there is no unique answer for the length of the sides of the rhombus.
Therefore, we cannot determine the length of a side of the rhombus with only the information provided.