The perimeter of a rhombus whose diagonals are 10cm and 24cm is
- A120cm
- B34cm
- C68cm
- D52cm
Solution & Step-by-step Explanation
Let the lengths of the two diagonals of the rhombus be d
1
=10cm and d
2
=24cm.
A property of a rhombus states that its diagonals bisect each other at right angles (90
∘
). This splits the interior into four symmetrical right-angled triangles.
The relationship connecting side length (s) and diagonals (d
1
,d
2
) using the Pythagorean theorem is:
s=
(
2
d
1
)
2
+(
2
d
2
)
2
Substitute the diagonal values:
s=
(
2
10
)
2
+(
2
24
)
2
s=
(5)
2
+(12)
2
s=
25+144
=
169
=13cm
The perimeter of a rhombus with four equal sides is:
Perimeter=4×s=4×13cm=52cm
1
=10cm and d
2
=24cm.
A property of a rhombus states that its diagonals bisect each other at right angles (90
∘
). This splits the interior into four symmetrical right-angled triangles.
The relationship connecting side length (s) and diagonals (d
1
,d
2
) using the Pythagorean theorem is:
s=
(
2
d
1
)
2
+(
2
d
2
)
2
Substitute the diagonal values:
s=
(
2
10
)
2
+(
2
24
)
2
s=
(5)
2
+(12)
2
s=
25+144
=
169
=13cm
The perimeter of a rhombus with four equal sides is:
Perimeter=4×s=4×13cm=52cm