The perimeter of a rhombus is 40 cm, and the length of one of its diagonals is 16 cm.
Therefore, the length of the other diagonal is: A) 12 cm B) 10 cm C) 8 cm D) 6 cm
The perimeter of a rhombus is 40 cm, and the length of one of its diagonals is 16 cm.
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To find the length of the other diagonal of the rhombus, we can use some properties of rhombuses:
1. The perimeter of a rhombus is given by the formula: (P = 4s), where (s) is the length of a side. In this case, we know the perimeter is 40 cm, so:
[
4s = 40 implies s = 10 text{ cm}
]
2. The diagonals of a rhombus bisect each other at right angles (90 degrees). Let’s denote the diagonals as (d_1) and (d_2). Given (d_1 = 16) cm, it will be halved to (8) cm for our calculations.
3. We can represent each half of the diagonals related to the sides of the rhombus using the Pythagorean theorem:
[
s^2 = left(frac{d_1}{2}right)^2 + left(frac{d_2}{2}right)^2
]
Substituting the known values:
[
10^2 = 8^2 + left(frac{d_2}{2}right)^2
]
[
100 = 64 + left(frac{d_2}{2}right)^2