Question

find the side of the square whose area is the same as that of the rhombus of diogonals 16cm and 32cm​

Answer 1

Gɪᴠᴇɴ :-

• Find the side of the square whose area is the same as that of the rhombus of diagonals 16cm and 32cm.

ᴛᴏ ғɪɴᴅ :-

• Side (a) of Square

sᴏʟᴜᴛɪᴏɴ :-

We know that,

$\implies \sf \: Area \: of \: Rhombus = \frac{1}{2} \times( Product \: of \: it's \: Diagonals) \\ \\ \\ \implies \tt \: \frac{1}{2} \times (16 \times 32) \\ \\ \\ \implies \tt \: \frac{512}{2} \\ \\ \\ \implies \tt \: 256 {cm}^{2}$

Now,

• Area of Rhombus = 256 cm²

And

• Area of Square = Area of Rhombus

• Area of Square = 256 cm²

➮ Area of Square = a² = 256

➮ a² = 256

➮ a = √256

➮ a = 16 cm

Hence,

• Side (a) of Square is 16 cm