A guy attached a wire 24 m long to a vertical pole of height 18 m and has a stake attached to other end. How far from the base of the pole should the stake be driven so that the wire will be taught ?

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.

If the sides of the triangle are in the ratio 3 : 4 : 5, prove that it is right-angled triangle.

For going to a city B from the city A, there is route via city C such that AC ⊥ CB. AC = 2x km and CB = 2(x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of highway.