One diagonal of a rhombus is half the other. If the length of the side of the rhombus is 10cm, what is the area of the rhombus?
- A40 sq cm
- B20 sq cm
- C100 sq cm
- D80 sq cm
Solution & Step-by-step Explanation
Let the longer diagonal be d
1
=2x. Then the shorter diagonal is d
2
=x.
The diagonals of a rhombus bisect each other at right angles. Therefore, the halves of the diagonals form the legs of a right-angled triangle with the side of the rhombus acting as the hypotenuse.
(
2
d
1
)
2
+(
2
d
2
)
2
=side
2
x
2
+(
2
x
)
2
=10
2
x
2
+
4
x
2
=100
4
5x
2
=100
5x
2
=400
x
2
=80
The formula for the area of a rhombus is:
Area=
2
1
×d
1
×d
2
Area=
2
1
×(2x)×x=x
2
Since x
2
=80, the area of the rhombus is 80sq cm.
1
=2x. Then the shorter diagonal is d
2
=x.
The diagonals of a rhombus bisect each other at right angles. Therefore, the halves of the diagonals form the legs of a right-angled triangle with the side of the rhombus acting as the hypotenuse.
(
2
d
1
)
2
+(
2
d
2
)
2
=side
2
x
2
+(
2
x
)
2
=10
2
x
2
+
4
x
2
=100
4
5x
2
=100
5x
2
=400
x
2
=80
The formula for the area of a rhombus is:
Area=
2
1
×d
1
×d
2
Area=
2
1
×(2x)×x=x
2
Since x
2
=80, the area of the rhombus is 80sq cm.