question_answer

Aryan wants to plant a flower on the ground in the form of a rhombus. The diagonals of the rhombus measures 42 cm and 56 cm. Find the perimeter of the field.

A)  \[150\text{ }cm\]                   

B)  \[140\text{ }cm\]       

C)         \[130\,cm\]                 

D)         \[120\,cm\]     

Correct Answer: B

Solution :

Since diagonals of a rhombus bisect each other at \[{{90}^{o}}\]. Given: \[BD=42\text{ }cm\]and \[AC=56\text{ }cm\]             \[\therefore \]    \[BK=\frac{1}{2}BD=\frac{42}{2}=21\,cm\]             \[AK=\frac{1}{2}AC=\frac{56}{2}=28\,cm\] In  \[\Delta \,KAB,\,\,\,A{{B}^{2}}=A{{K}^{2}}+B{{K}^{2}}\] \[={{(28)}^{2}}+{{(21)}^{2}}=784+441=1225\] \[\therefore \]  \[AB=\sqrt{1225}\,=\,35\,cm\] \[\therefore \] Perimeter of the field \[ABCD=4\times 35=140\text{ }cm\];