# The Perimeter of a Rhombus is 60 Cm. If One of Its Diagonal Us 18 Cm Long, Find (I) the Length of the Other Diagonal, and (Ii) the Area of the Rhombus. - Mathematics

The perimeter of a rhombus is 60 cm. If one of its diagonal us 18 cm long, find

(i) the length of the other diagonal, and

(ii) the area of the rhombus.

#### Solution

Perimeter of a rhombus = 4a (Here, a is the side of the rhombus)

⇒ 60=4a

⇒ a=15

(i) Given:

One of the diagonals is 18 cm long

d_1= 18cm

Thus, we have:

Side= 1/2sqrt(d_1^2+d_2^2)

⇒ 15=1/2sqrt(18^2+d_2^2)

⇒30=sqrt(18^2+d_2^2)

Squaring both sides, we get:

⇒900=18^2+d_2^2

⇒900=324+d_2^2

⇒d_2^2=576

⇒d_2^2=24cm

(ii) Area of the rhombus=1/2d_1xxd_2

=1/2xx18xx24

=216 cm^2

Concept: Circumference of a Circle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 17 Perimeter and Areas of Plane Figures
Q 33