In rhombus,
Problem 1 :
Find the side length of rhombus given.
Solution :
Since the given shape is rhombus, all sides will have equal measure.
AD = DC
5x + 4 = 2x + 13
5x - 2x = 13 - 4
3x = 9
x = 9/3
x = 3
Applying the value of x, we get
AD = 5(3) + 4
AD = 15 + 4
AD = 19
Problem 2 :
Find the side length of the rhombus ABCD.
Solution :
Let E be the point of intersection of two diagonals. Considering the triangle DEC,
DE = 20 ft, EC = 30 ft
DC^{2} = DE^{2} + EC^{2}
DC^{2} = 20^{2} + 30^{2}
DC^{2} = 400 + 900
DC^{2} = 1300
DC = 10√13
Problem 3 :
The area of a rhombus is 150 cm^{2}. The length of one of its diagonal is 10 cm. The length of their other diagonal is .
(a) 25 cm (b) 30 cm (c) 35 cm (d) 40 cm
Solution :
Area of rhombus = (1/2) x d_{1} x d_{2}
(1/2) x 10 x d_{2 }= 150
d_{2} = 150 / 5
d_{2} = 30 cm
Problem 4 :
One of the diagonals of a rhombus is double the other diagonal. Its area is 25 sq.cm. The sum of the diagonal is
(a) 10 cm (b) 12 cm (c) 15 cm (d) 16 cm
Solution :
d_{1} = 2d_{2}
(1/2) x d_{1} x d_{2} = 25
(1/2) x 2d_{2} x d_{2} = 25
d_{2}^{2} = 25
d_{2} = 5
then d1 = 2(5) ==> 10 cm
Sum of the diagonals = 10 + 5 ==> 15 cm
Problem 5 :
The perimeter of a rhombus is 56 m and height is 5 m. Its area is.
(a) 64 sq.cm (b) 70 sq.cm (c) 78 sq.cm (d) 84 sq.cm
Solution :
Perimeter of rhombus (4a) = 56
a = 56/4
a = 14 cm
height = 5 cm
Area of rhombus = base x height
= 14 x 5
= 70 sq.cm
Problem 6 :
If the diagonals of a rhombus are 24 cm and 10 cm, find the area and perimeter of rhombus.
Solution :
Area of rhombus = (1/2) x d_{1} x d_{2}
d_{1} = 24 cm and d_{2} = 10 cm
= (1/2) x 24 x 10
= 120 square cm
To find perimeter of rhombus, we should find the side length of rhombus.
side^{2} = 12^{2} + 5^{2}
side^{2} = 144 + 25
side^{2} = 169
= √169
= 13
Perimeter of rhombus = 4(13)
= 52 cm
Problem 7 :
Each side of a rhombus is 26 cm and one of its diagonal is 48 cm long. The area of the rhombus is.
(a) 240 cm^{2 }(b) 300 cm^{2 }(c) 360 cm^{2 }(d) 480 cm^{2}
Solution :
The diagonals will bisect each other at right angle.
Half length of given diagonal = 24
half length of another diagonal = x
26^{2} = 24^{2} + x^{2}
676 = 576 + x^{2}
x^{2} = 676 - 576
x^{2} = 100
x = 10
Length of another diagonal = 20
Area of rhombus = (1/2) x 48 x 20
= 480 square cm
Problem 8 :
The length one diagonal of a rhombus is 80% of the other diagonal. The area of the rhombus is how many times the square of length of the other diagonal ?
(a) 4/5 (b) 2/5 (c) 3/4 (d) 1/4
Solution :
Let d_{1} and d_{2} be length of diagonals.
d_{1} = 80% of d_{2 }==> 0.80d_{2}
Area of rhombus = (1/2) x 0.80d_{2 }x d_{2}
= (1/2) x 0.80(d_{2})^{2}
= 0.40(d_{2})^{2}
= (40/100)(d_{2})^{2}
= 2/5(d_{2})^{2}
So, the answer is 2/5.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM