One diagonal of a rhombus is 20cm. long and its area is 100 cm2. Find the length of a side of the rhombus

Question

Geometry help on homework

Answer 1

Diagonal a*diagional b/2=area of rhombus 

20*b/2=100

20b/2=100

10b=100

b=100/10

b=10

 

the second diagional is 10cm.

 

formula for side=

square root of a^2+b^2/2

 

20^2+10^2/2

 

side=square root of 500/2

side= square root of 125

side=11.18

Answer 2

The area of a rhombus is one half the product of its diagonals

 

A=pq/2

 

using the given area and one diagonal we can find the other diagonal

 

100=20q/2

q=10 cm 

p=20 cm 

 

the diagonals intersect at right angles. So using Pythagorean theorem where each leg is one half of each diagonal We can compute the side length. A rhombus has four equal sides. The hypotenuse in our Pythagorean theorem is one of the rhombus sides. 

 

5² + 10² = s² 

125 = s² 

 

s=5•sqrt(5) cm