Question

The length of a side of a square field is 4 m. What will be the altitude of the rhombus, if the area of the rhombus is equal to the square field and one of its diagonal is 2 m?

Answer 1

Length of side of a square $=4m$

Area of square $=(side{)}^2$

$=(4{)}^2$

$=16m^2$

It is given that,

Area of square $=$ Area of rhombus

$\therefore$ Area of rhombus $=16m^2$

Area of rhombus $=\frac{d_1{d}_2}{2}$

$\Rightarrow$ $16=\frac{1}{2}\times 2\times d_2$

$\Rightarrow$ $d_2=16$

$\therefore$ The diagonal of rhombus $=16m$

Using Pythagoras theorem :

$A{B}^2=O{A}^2+O{B}^2$

$A{B}^2=8^2+1^2$

$A{B}^2=65$

$AB=\sqrt{65}$

Since, rhombus is a parallelogram,

$\therefore$ area of parallelogram $=AB\times DE$

$\Rightarrow$ $16=\sqrt{65}\times DE$

$\Rightarrow$ $DE=\frac{16}{\sqrt{65}}cm$