Question

The diagonal of a square is 4$\sqrt{2}$cm. The perimeter of the square and a triangle is same. Find the semi perimeter of the triangle. [3 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

The diagonal of the square = 4$\sqrt{2}$ cm

Now let the side of the square = a cm

By Pythagoras theorem

$(4\sqrt{2}{)}^2=a^2+a^2$
$\Rightarrow$ a = 4cm

Perimeter of the square = 4a = 16cm

Perimeter of the square = Perimeter of triangle

$\Rightarrow$ Semi perimeter of the triangle = $\frac{16}{2}$ = 8cm