Note: Relation between the areas of two similar triangles: If then

Question 1: (i) The ratio between the corresponding sides of two similar triangles is Find the ratios between the areas of these triangles.

(ii) Areas of two similar triangles is Find the ratios between the length of their corresponding sides.

Answer:

Question 2: A line is drawn parallel to the base which meets sides at points respectively. If ; find the value of

Answer:

(AAA postulate)

Question 3: The perimeter of two similar triangles are If one side of the first triangle is , determine the corresponding side of the second triangle.

Answer:

Since the two given triangles are similar, we have

Question 4: In the given figure, Find:

(i) the length of , if the length of is

(ii) the ratio between the areas of trapezium

Answer:

Question 5: is a triangle. is a line segment intersecting such that and divides into two parts equal in area. Find the value of ratio

Answer:

(corresponding angles)

Question 6: In the Calculate the value of the ratio:

Answer:

(ii) Since have common vertex and their bases are along the same straight line

(iii) Since have common vertex and their bases are along the same straight line

Question 7: The given diagram shows two isosceles triangles which are similar. are not parallel. Calculate:

(i) the length of

(ii) the ratio of the areas of

Answer:

Since

Solving

Question 8: In the figure given below, is a parallelogram. is a point on such that produced meets produced at Given the area of Calculate:

(i) area of

(ii) area of parallelogram **[1996]**

Answer:

(i) In

(ii) In

(corresponding angles are equal)

Question 9: In the given figure, Area of , area of trapezium Calculate the length of Also find the area of

Answer:

Question 10: The given figure shows a trapezium in which and diagonals intersect at point If Find:

Answer:

(i) Since have common vertex and their bases are along the same straight line

(ii) Since

(iii) Since have common vertex and their bases are along the same straight line

(iv) Since have common vertex and their bases are along the same straight line

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:

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:

(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

Answer:

(ii) In

(iii) We know

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

Answer:

(Since is common and is given)

We know that for similar triangles

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

Answer:

(Since angles opposite equal sides are also equal)

We know that for similar triangles

(ii) Now

(given)

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

wold represent of actual airplane

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