Question

The diagonal of a square is $6\sqrt{2}$ cm.The perimeter of the square and a triangle is same.Find the semi perimeter of the triangle.

• A. 8 cm
• B. 12 cm
• C. 10 cm
• D. 14 cm

Answer 1

The correct option is B

12 cm

Diagonal of the square = $6\sqrt{2}$ cm

Let the side of the square be a.

By Pythagoras theorem,

$\left(6\sqrt{2}{)}^2\right)=a^2+a^2=2a^2$
$\Rightarrow$ $a$ = 6 cm

Perimeter of the square = 4a = 24 cm

Perimeter of the square = Perimeter of triangle

Semi perimeter of the triangle = $\frac{24}{2}$ = 12 cm