The perimeters of two similar triangles are ^@ 35 \space cm^@ and ^@25 \space cm^@ respectively. If one side of the first triangle is ^@70 \space cm^@, find the corresponding side of the second triangle.
In the given figure, ^@ AB ^@ is a chord of length ^@ 9 \space cm ^@ of a circle with center ^@ O ^@ and radius ^@ 5 \space cm ^@. The tangents at ^@ A ^@ and ^@ B ^@ intersect at ^@ P ^@. What is the length of ^@ PA ^@?
A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in the figure.The height of the entire rocket is 26 cm, while the height of the conical part is 21 cm. The base of the conical portion has a diameter of 9 cm,which the base diameter of the cylinderical portion is 7 cm. If the conical portion is painted blue , choose the area of the rocket painted with blue colours.
A monkey sitting at a height of ^@ 12 \space m ^@ on a tall tree on a small island in the middle of a river observers two poles directly opposite each other on the two banks of the river and in line with the foot of the tree. If the angles of depression of the feet of the poles from a point at which the monkey is sitting on the tree on either side of the river are ^@ 60^\circ ^@ and ^@ 45^\circ ^@ respectively. What is the width of the river?