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RD Chapter 4 Triangles Ex 4.6 Solutions

Question - 11 : - The areas of two similar triangles are 121 cm² and 64 cm² respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other. (C.B.S.E. 2001)

Answer - 11 : -

∆ABC ~ ∆DEF
area of ∆ABC = 121 cm² area of ∆DEF = 64 cm²
AL and DM are the medians of ∆ABC and ∆DEF respectively
AL = 12.1 cm

Question - 12 : - In ∆ABC ~ ∆DEF such that AB = 5 cm and (∆ABC) = 20 cm² and area (∆DEF) = 45 cm², determine DE.

Answer - 12 : -

∆ABC ~ ∆DEF
area (∆ABC) = 20 cm²
area (∆DEF) = 45 cm²

Question - 13 : - In ∆ABC, PQ is a line segment intersecting AB at P and AC at Q such that PQ || BC and PQ divides ∆ABC into two parts equal in area. Find BP/AB.

Answer - 13 : -

In ∆ABC, PQ || BC and PQ divides ∆ABC in two parts ∆APQ and trap. BPQC of equal in area
i.e., area ∆APQ = area BPQC

Question - 14 : - The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR. (C.B.S.E. 2004)

Answer - 14 : -

∆ABC ~ ∆PQR
area (∆ABC) : area (∆PQR) = 9 : 16
and BC = 4.5 cm

Question - 15 : - ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ∆APQ is one sixteenth of the area of ∆ABC. (C.B.S.E. 2005)

Answer - 15 : -

In ∆ABC, P and Q are two points on AB and AC respectively such that
AP = 1 cm, PB = 3 cm, AQ = 1.5 cm and QC = 4.5 cm

Question - 16 : - If ∆ABC and ∆BDE are equilateral triangles, where D is the mid point of BC, find the ratio of areas of ∆ABC and ∆BDE. [CBSE 2010]

Answer - 16 : - ∆ABC and ∆DBE are equilateral triangles Where D is mid point of BC

Question - 17 : - Two isosceles triangles have equal vertical angles and their areas are in the ratio 36 : 25. Find the ratio of their corresponding heights.

Answer - 17 : -

Two isosceles triangles have equal vertical angles
So their base angles will also be the equal to each other
Triangles will be similar Now, ratio in their areas = 36 : 25

Question - 18 : - In the figure, ∆ABC and ∆DBC are on the same base BC. If AD and BC intersect

Answer - 18 : -

Given : Two ∆ABC and ∆DBC are on the same base BC as shown in the figure
AC and BD intersect eachother at O

Question - 19 : -
ABCD is a trapezium in which AB || CD. The diagonals AC and BD intersect at O. Prove that
(i) ∆AOB ~ ∆COD
(ii) If OA = 6 cm, OC = 8 cm, find

Answer - 19 : -

Given : ABCD is a trapezium in which AB || CD
Diagonals AC and BD intersect each other at O

Question - 20 : - In ∆ABC, P divides the side AB such that AP : PB = 1 : 2. Q is a point in AC such that PQ || BC. Find the ratio of the areas of ∆APQ and trapezium BPQC.

Answer - 20 : -

In ∆ABC, P is a point on AB such that AP : PQ = 1 : 2
PQ || BC
Now we have to find the ratio between area ∆APQ and area trap BPQC

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