Question

The length of a side of a square field is 4 cm. what wil be the altitude of rhombus , if the area of the rhombus is equal to the square field and one of the diagonal is 2 cm?

Answer 1

Area of Rhombus = Area of square

$=(4{)}^{2}cm$

$=16sq.cm$

Area of Rhobus $=\frac{1}{2}\times d_1\times d_2$

$16sqcm=\frac{1}{2}\times 2cm\times d_2$

$\therefore d_2=16cm$

We know that Area of Rhombus $=side\times attitude$

of side $=\frac{1}{2}\sqrt{d_2^2+d_2^2}$

$=\frac{1}{2}\sqrt{4+256}$

$=\frac{1}{2}\sqrt{260}$

$\therefore Altitude=\frac{AreaofRhombus}{side}$

$=\frac{16sqcm}{\frac{1}{2}\sqrt{260}m}$

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