Question

the length of the diagonal of a rhombus are 24cm and 10 cm respectively.find the side of the rhombus. step by step pls​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A Rhombus
• Having a diagonals
• 24 and 10

${\sf{\green{\underline{\large{To\:find}}}}}$

• Side of the Rhombus

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Property of Rhombus

• Diagonals of Rhombus
• Bisect it at Right angle

So using this property we find

Here,

In right ∆ DOA

angle ODA =90°

Or

BD=24

OD=1/2 ×AD= 12

AC=10

OA=5

Using Pythagoras Theorm

OD²+OA²=AD²

¶utting values

(12)²+(5)²=AD²

=>AD²=144+25

=>AD²=169

=>AD=√169

=>AD=13

Here side of Rhombus are equals

Therefore side of Rhombus is 13

Answer 2

★ DIAGRAM:-

$\setlength{\unitlength}{2mm}\begin{picture}(5,5)\put(0,0){\line(1,0){24}}\put(12,-6){\line(0,1){12}}\multiput(0,0)(12,-6){2}{\line(2,1){12}}\multiput(24,0)(-12,-6){2}{\line(-2,1){12}}\put(14,-1.6){\footnotesize\textsf{24\ cm}}\put(7.8,2){\footnotesize\textsf{10\ cm}}\end{picture}$

★ GIVEN:-

• Diagonal 1 ( d₁ ) = 24cm
• Diagonal 2 ( d₂ ) = 10 cm

★ TO FIND:-

• Side of rhombus = ?

★ SOLUTION:-

Finding : - d₁/2 & d₂/2

d₁/2 = 24/2 = 12 cm

d₂/2 = 10/2 = 5 cm

Properties of rhombus:

• All sides are equal
• Diagonals bisect perpendicularly each other

We got a right angled triangle with base 5cm & height 12cm

That means here hypotenuse = side of rhombus

Using Pythagoras theorem and finding the hypotenuse

(Hypotenuse)² = (Base)² + (Height)²

Side² = 5² + 12²

Side = √169

Side = 13 cm

Since all sides of rhombus are equal then all sides = 13cm

Hence , length of each side of rhombus = 13cm