# APPLYING PROPERTIES TO FIND SIDE LENGTH OF RHOMBUS

In rhombus,

• All sides are equal.
• Diagonals will bisect each other at right angles,
• The diagonals are equal.

Problem 1 :

Find the side length of rhombus given. Solution :

Since the given shape is rhombus, all sides will have equal measure.

5x + 4 = 2x + 13

5x - 2x = 13 - 4

3x = 9

x = 9/3

x = 3

Applying the value of x, we get

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

DC2 = DE2 + EC2

DC2 = 202 + 302

DC2 = 400 + 900

DC2 = 1300

DC = 10√13

Problem 3 :

The area of a rhombus is 150 cm2. 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 d1 x d2

(1/2) x 10 x d2 = 150

d2 = 150 / 5

d2 = 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 :

d1 = 2d2

(1/2) x d1 x d2 = 25

(1/2) x 2d2 x d2 = 25

d22 = 25

d2 = 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 d1 x d2

d1 = 24 cm and d2 = 10 cm

= (1/2) x 24 x 10

= 120 square cm

To find perimeter of rhombus, we should find the side length of rhombus.

side2 = 122 + 52

side2 = 144 + 25

side2 = 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 cm2       (b) 300 cm2  (c) 360 cm2    (d) 480 cm2

Solution :

The diagonals will bisect each other at right angle.

Half length of given diagonal = 24

half length of another diagonal = x

262 = 242 + x2

676 = 576 + x2

x2 = 676 - 576

x2 = 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 d1 and d2 be length of diagonals.

d1 = 80% of d==> 0.80d2

Area of rhombus = (1/2) x 0.80dx d2

= (1/2) x 0.80(d2)2

= 0.40(d2)2

= (40/100)(d2)2

= 2/5(d2)2

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