Puzzle 47

Semi circles are drawn on each side of a square. An elastic band is stretched tightly around the shape formed (see the figure). Find the length of the elastic band in terms of the length x, of the side of the square.

Puzzle 46 - Squares

Square ABCD, of side length 26, is centered at O. With D as center, draw another square EFGH with side length 22, none of its sides parallel to those of ABCD, so that OE is kept perpendicular to DA. Find the area of the square ABCD that is not inside the square EFGH.

Puzzle 45 - Similar Triangles

Let A is the set of all triangles in a plane. Define a function as implies that triangle is similar to with the dilation constant or scale factor ‘a’. Find all the possible triangles and such that

a. Lengths of the sides of and are integers
b. The perimeter and area of are same.

Puzzle 44

W(a, b) is the centre of the circle. TE is a tangent to the circle at E, which lies on the y-axis. The circle touches the x-axis at D. The equation of TE is. Calculate the values of a and b.