Question
Rhombus ABCD is shown below.
one leg is 6
the other leg is 8
What is the perimeter of the rhombus?
10 units
14 units
40 units
96 units
one leg is 6
the other leg is 8
What is the perimeter of the rhombus?
10 units
14 units
40 units
96 units
Answers
GPT-4o mini
In a rhombus, all four sides are equal in length. However, you mentioned two legs (6 and 8), which suggests that you might be referring to a right triangle formed by the diagonals of the rhombus.
To clarify, if you have legs of 6 and 8, you can find the length of each side of the rhombus using the Pythagorean theorem. The relationship is as follows:
\[
\text{Side} = \sqrt{(6^2 + 8^2)} = \sqrt{(36 + 64)} = \sqrt{100} = 10
\]
Since the sides of the rhombus are each 10 units long, the perimeter \(P\) of the rhombus can be found by multiplying the length of one side by 4:
\[
P = 4 \times 10 = 40 \text{ units}
\]
Thus, the perimeter of the rhombus is **40 units**.
To clarify, if you have legs of 6 and 8, you can find the length of each side of the rhombus using the Pythagorean theorem. The relationship is as follows:
\[
\text{Side} = \sqrt{(6^2 + 8^2)} = \sqrt{(36 + 64)} = \sqrt{100} = 10
\]
Since the sides of the rhombus are each 10 units long, the perimeter \(P\) of the rhombus can be found by multiplying the length of one side by 4:
\[
P = 4 \times 10 = 40 \text{ units}
\]
Thus, the perimeter of the rhombus is **40 units**.