$A$ ladder is resting with one end in contact with the top of a wall of height $12\, m$ and the other end on the ground is at a distance $5\, m$ from the wall. The length of the ladder is.....$m$

$A$ farmer wishes to start a $100 \, m^2$ rectangular vegetable garden. Since he has only $30 \, m$ of barbed wire,he fences three sides of the garden,using his house compound wall as the fourth side. The dimensions of the garden are:

The breadth of a rectangular plot is $75 \%$ of its length. If the perimeter of the plot is $1050 \, m,$ what is its area (in $, m^2$)?

If the perimeter of a right-angled isosceles triangle is $4 \sqrt{2}+4 \,m ,$ then the hypotenuse is.........$m$

Find the area of an isosceles right-angled triangle whose hypotenuse is $8\, cm$.

The diameter of a circle circumscribing a square is $10 \, cm$. Its sides will be