the length of the two digonal of a rhombs are 6 cm and 8cm respectively . what is the length of its side ?
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Question - the length of the two digonal of a rhombs are 6 cm and 8cm respectively . what is the length of its side ?
Answer -
The diagonals of a rhombus are perpendicular
to each other and, at the same time, they bisect
each other; consequently, four (congruent
right triangles are formed by the two intersecting
diagonals as well as the sides of the rhombus,
as the four sides of a rhombus are congruent,
i.e., all four have the same length; consequently,
we have four congruent right triangles, each with
legs measuring 3 cm (one-half of the
6 cm-diagonal) and 4 cm (one-half of the 8
cm-diagonal); The length of the remaining side,
the hypotenuse, we are required to determine
because that length is also the length of each
side of the given rhombus.
Since we're dealing with right triangles, we can
use the equation of the Pythagorean Theorem
to find the length of the desired remaining side
of each right triangle, i.e., the hypotenuse, and,
therefore, the length of each side of the given
rhombus:
a² + b² = c², where a and b are the lengths of the
two shorter sides (legs) of a right triangle, and c
is the length of the longest side, the hypotenuse.
Substituting, we get:
(3 cm)² + (4 cm)² = c²
9 cm² + 16 cm² = c^2
25 cm² = c²
±√(25 cm²) =√c²
√(25 cm²) =√c² (Note: The positive square root
was chosen since you physically can't have a
negative length)
5 cm = c
Therefore, the length of each side s of the given