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