Question 11: On a map drawn to a scale of a triangular plot of of land has the following measurements: . Calculate:

(i) the actual length of in kilometers

(ii) the actual area of the plot in

Answer:

Scale factor

(i) Length of side in the map = the actual length of the side in the land

Length of side in the map the actual length of the side in the land

actual length of

Hence

(ii) Area of the plot

Question 12: A model of a ship is made to scale of .

(i) The length of the model is ; calculate the length of the ship.

(ii) The area of the deck of the ship is ; find the area of the deck of the model.

(iii) The volume of the model is ; calculate the volume of the ship in . **[1995]**

Answer:

Scale factor

(i) Length of the model Actual length of the ship

Actual length of the ship

(ii) Area of the deck of the model area of the deck of the actual ship

(iii) Volume of the model Volume of the actual ship

Question 13: In the figure given below is a triangle. is parallel to and .

(i) Determine the ratios

(ii) Prove that is similar to . Hence , find . ** [2007]**

Answer:

(i) Given

(common angle)

(ii) In

(alternate angles)

(vertically opposite angles)

(iii) We know

Question 14: In the given figure , . . Find the ratio between the area of the .

Answer:

Consider

(Since is common and is given)

Therefore

We know that for similar triangles

Question 15: is an isosceles triangle in which and . If , find:

(i)

(ii)

Answer:

(i) Consider

(Since angles opposite equal sides are also equal)

Therefore

We know that for similar triangles

(ii) Now Consider

(given)

Therefore

Therefore

Question 16: An airplane is long and its model is long. If the total outer surface area of the model is , find the cost of painting the outer surface of the airplane at the rate of . Given that of the surface of the airplane sis left for windows.

Answer:

of the model represent of actual airplane

Therefore wold represent of actual airplane

Hence would represent of the surface are of the actual airplane

Given that the surface area of the model .

Therefore the actual surface are of the actual airplane

Area to be painted

Cost of painting

Therefore the total cost of painting