"If diagonals of a rhombus are 10cm and..." was answered by our community

caigis72da

Answered question

2023-03-22

If diagonals of a rhombus are

10 c m

and

24 c m

, find its perimeter.

Desiree Cantrell

Beginner2023-03-23Added 3 answers

Step 1: Given is a rhombus.
The diagonals

A C

and

B D

are of length

10 c m

and

24 c m

respectively.

Step 2: Find the lengths of

O B

and

O C

.
A rhombus has diagonals that are at right angles to one another.

O B = \frac{1}{2} (B D) \Rightarrow O B = \frac{1}{2} (24) = 12

O C = \frac{1}{2} (A C) \Rightarrow O C = \frac{1}{2} (10) = 5

Step 3: Find the length of

B C

.
Use the Pythagoras theorem, to find the length of

B C

{(B C)}^{2} = {(O B)}^{2} + {(O C)}^{2} {\Rightarrow (B C)}^{2} = 12^{2} + 5^{2} {\Rightarrow (B C)}^{2} = 144 + 25 \Rightarrow {(B C)}^{2} = 169 \Rightarrow B C = 13 (S q u a r e r o o t o f 169 i s 13)

Step 4: Find the perimeter of rhombus.
All the four sides of a rhombus are equal.

P e r i m e t e r = 4 \times s i d e = 4 \times B C = 4 \times 13 = 52

Hence, the perimeter of the rhombus with diagonals

10 c m

and

24 c m

52 c m

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?