Ex 6.5, 8 The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter
In a rhombus
All sides are equal
Diagonals are perpendicular
Let ABCD be the given rhombus
Where
BD = 16 cm
and AC = 30 cm
We know that,
Diagonals of rhombus are perpendicular bisector of each other
∴ AC ⊥ BD
And
OB = 𝐵𝐷/2
= 16/2
= 8 cm
OA = 𝐴𝐶/2
= 30/2
= 15 cm
Now,
In ∆AOB, right angled at O,
By Pythagoras Theorem,
〖𝐴𝐵〗^2 = 〖(𝑂𝐴)〗^2 + 〖(𝑂𝐵)〗^2
〖𝐴𝐵〗^2 = 〖(15)〗^2 + 〖(8)〗^2
〖𝐴𝐵〗^2 = 225 + 64
〖𝐴𝐵〗^2 = 289
〖𝐴𝐵〗^2 = 〖(17)〗^2
Cancelling square
AB = 17 cm
Now,
Perimeter ABCD = AB + BC + CD + AD
= AB + AB + AB + AB
= 4 × AB
= 4 × 17 = 68 cm
Hence, required perimeter is 68 cm
(Since sides of rhombus are equal)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

Hi, it looks like you're using AdBlock :(

Displaying ads are our only source of revenue. To help Teachoo create more content, and view the ad-free version of Teachooo... please purchase Teachoo Black subscription.

Please login to view more pages. It's free :)

Teachoo gives you a better experience when you're logged in. Please login :)

Solve all your doubts with Teachoo Black!

Teachoo answers all your questions if you are a Black user!