Question

State true or false.

The diagonal of a square is $15$ m, then the length of its one side is $10.6$ m

• A. True
• B. False

Answer 1

The correct option is A True

Let the side of the square $=a$ m.

The diagonal of a square divides it into two equal right-angled triangles.

Hence, diagonal forms the hypotenuse of a right-angled triangle, with the other two sides being the sides of the square.

Hence, diagonal $=\sqrt{a^2+a^2}$

$d=\sqrt{2}a$; where $a$ is side of square.

$\therefore 15=\sqrt{2}a$.

$a=\frac{15}{\sqrt{2}}=\frac{15\sqrt{2}}{2}=10.6m$