Question

A wire when bent in the form of a square, encloses an area of 900 cm². When this wire is bent in the form of equilateral triangle, its area becomes:

Options

• `400sqrt(3)` cm²

• `300sqrt(3)` cm²

• `200sqrt(3)` cm²

• `100sqrt(3)` cm²

Answer 1

`bb(400sqrt(3)  cm^2` 

Explanation:

Square area = 900 cm² 

⇒ Side = `sqrt(900)`

= 30 cm

So, wire length (perimeter)

= 4 × 30

= 120 cm

Bent as an equilateral triangle, each side

= `120/3`

= 40 cm

Triangle area

= `sqrt(3)/4 xx "side"^2` 

= `sqrt(3)/4 xx 40^2`

= `sqrt(3)/4 xx 1600`

= `400sqrt(3)  "cm"^2`