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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

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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.

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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
  Is there an error in this question or solution?

APPEARS IN

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