Question

A ladder 6.5 m long leans against a vertical wall and reaches a point 6 m above the ground, as shown. How far is the foot of the ladder from the wall (in m)?

Two members of a Pythagorean triplet are 12 and 37. Using the form 2m,\ m^2 - 1,\ m^2 + 1, find the third member.

A gram panchayat builds a rectangular playground 48 m long and 20 m wide, with a straight path along one diagonal (see figure). Next to it, a square kitchen garden of area 529\ \text{m}^2 is made.