Question

area of a rhombus is 96cm². If one of its diagonals is 16cm the find out length of the side

Answer 1

hope this helps you.....

Answer 2

Answer:  

Property of rhombus : Diagonal of rhombus is perpendicular to each other and also bisect each other.

To, find the Area of a rhombus(A), multiply the lengths of the two diagonals and divide by 2.

i.e, $A =\frac{d_1 \times d_2}{2}$ where $d_1$ , $d_2$ are two diagonals of rhombus.     ......[1]

Given:  Area of rhombus(A) = 96 $cm^2$ and one of its diagonal ,let ($d_1$ ) = 16 cm.

Substitute these in [1] to get another diagonal $d_2$ ;

then,

$96 = \frac{16 \times d_2}{2}$ or

$192 = 16 \times d_2$

Simplify:

$d_2= 12$ cm.

To find the length of one side of the rhombus,

Apply the formula:  $4a^2=d_1^2+d_2^2$ where a is the sides of the rhombus , $d_1$ and  $d_2$ are two diagonals of rhombus.

Substitute the value of diagonals we get;

$4a^2=(16)^2+(12)^2$ or

$4a^2=256+144 = 400$

Divide by 4 to both sides of an equation:

$\frac{4a^2}{4}= \frac{400}{4}$

Simplify:

$a^2 = 100$ or

$a= \sqrt{100} =10 cm$

Therefore, the length of the side of rhombus is, 10 cm