Question

Find the side of square which has the same area as rhombus of diagonals 12 cm and 13 . 5 cm

Answer 1

Answer :

9 cm

Step-by-step explanation :

Given that ;

Area of square = Area of rhombus

Now,

Diagonal (p) = 12 cm

Diagonal (q) = 13.5 cm

Area of rhombus = $\bf \frac{pq}{2}$

                             = $\sf \frac{pq}{2}$

                            = $\sf \frac{12\times13.5}{2}$

                            = $\sf \frac{162}{2}$

                            = 81

∴ Area of rhombus = 81 cm²

But, it is given that, the area of rhombus is equal to the area of square.

⇒ Area of square = 81 cm²

⇒ ( side² ) = 81 cm²

⇒ side = √81 cm

⇒ side = 9 cm

Hence, the side of square is 9 cm.

Answer 2

Given,

First diagonal of rhombus = 12 cm
Other diagonal of rhombus = 13.5 cm

Area of the rhombus = ( 1 / 2 ) * (Product of its diagonals)
=> Area of the rhombus = ( 1 / 2 ) * ( 12 * 13.5 )
=> Area of the rhombus = ( 1 / 2 ) * 162
=> Area of the rhombus = 81 sq. cm

Hence,

Area of rhombus = Area of square

Let, each side of square be 'x'.

Area of square = 81 sq. cm
x² = 81 sq. cm
x = √81
x = 9 cm

Therefore,

Each side of square = 9 cm