Question

A square and an equilateral triangle have the same perimeter . If the diagonal of square is 12√2cm . The show the area of triangle is 64√3cm×cm.

Answer 1

The diagonal of a square is given by the formula → ✓2 a

Therefore , ✓2a = 12✓2

or, a = 12✓2/✓2

or, a = 12cm

So, The side of square is 12cm.

Perimeter of square = 4(side)

= 4 × 12

= 48cm

According To Question→

Perimeter of square = Perimeter of Triangle

Perimeter of Triangle is 3(side)

Let, the side be x.

Therefore , 3x = 48

or , x = 48/3

or, x = 16

Area of Equilateral Triangle →

(✓3/4 )(side)²

= ✓3/4 × 16×16

= ✓3 × 4 × 16

= 64✓3 cm²

Hence Proved.
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Answer 2

Answer:

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