# WORD PROBLEMS ON SIMILARITY OF TRIANGLE

Word Problems on Similarity of Triangle :

Here we are going to see some practice problems based on the concept similar triangles.

## Word Problems on Similarity of Triangle-Questions

Question 1 :

In the adjacent figure, triangle ABC is right angled at C and DE  AB . Prove that ΔABC  ΔADE and hence find the lengths of AE and DE. In triangle ABC,

AB2  =  BC2 + AC2

AB2  =  122 + 52

AB2  =  144 + 25  =  169

AB  =  13

In triangles ABC and EAD

<BCA  =  <AED

<CAB  =  <DAE

So, the triangles ABC and EAD are similar.

BC/EA  =  CA/ED  =  AB/AD

12/EA  =  (2+3)/ED  =  13/3

12/EA  =  5/ED  =  13/3

12/EA  =  13/3

EA  =  36/13

5/ED  =  13/3

ED  =  5(3)/13

ED  =  15/13

Question 2 :

In the adjacent figure, ΔACB  ∼ ΔAPQ . If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Solution :

Since the triangles ACB and APQ are similar.

BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm

BC/PQ (Angles opposite to <BAC and <PAQ)  --(1)

AC/PA (Angles opposite to <ABC and <AQP) --(2)

AB/AQ (Angles opposite to <ACB and <APQ) --(3)

(1)  =  (2)  =  (3)

BC/PQ  =  AC/PA  =  AB/AQ

8/4  =  AC/2.8  =  6.5/AQ

8/4  =  AC/2.8

AC  =  8(2.8)/4

AC  =  5.6 cm

8/4  =  6.5/AQ

AQ  =  6.5(4)/8

AQ  =  3.25 cm

Question 3 :

If figure OPRQ is a square and <MLN = 90° . Prove that (i) ΔLOP ∼ ΔQMO (ii) ΔLOP ∼ ΔRPN (iii) ΔQMO ∼ ΔRPN (iv) QR2 = MQ × RN Solution :

(i) ΔLOP ∼ ΔQMO

In triangles ΔLOP  and ΔQMO

<OMQ  =  <LOP  (Corresponding angles)  A

<MQO  =  <OLP  (90)  A

OQ  =  OP  (side)

By ASA, the above triangles are similar.

(ii) ΔLOP ∼ ΔRPN

<LPO  =  <PNR  (corresponding angles) A

<OLP  =  <PRN  (90) A

OP  =  PR (side)

By ASA, the above triangles are similar.

(iii) ΔQMO ∼ ΔRPN

<OQM  =  <PRN  (A)

OQ  =  PR  (Side)

Since the triangles ΔLOP and ΔQMO are similar,

OP/MO  =  OL/OQ  =  LP/MQ

OP/PN  =  OL/RN  =  LP/PR

MQ  =  PR  ----(1)

OQ  =  RN  ----(2)

MQ  =  RN

Hence the ΔQMO ∼ ΔRPN.

(iv) QR2 = MQ × RN

Let us join OR,

OR2  =  OQ2 + QR2

OP2 + PR2 -  OQ2  =  QR2

OP2  =  QR2

OP  =  MQ =  RN

OP (OP)  =   QR2

MQ x RN  =  QR2

Hence proved.

Question 4 :

If ΔABC  ∼ ΔDEF such that area of ΔABC is 9cm2 and the area of ΔDEF is 16cm2 and BC = 2.1 cm. Find the length of EF.

Solution :

Since the ratio of area of two similar triangles is equal to the ratio of the squares of any two corresponding sides, we have

Area of ΔABC / Area of ΔDEF  =  BC2/EF2

(9/16)  =  (2.1)2/EF2

EF=  4.41 (16/9)

EF  =  2.8 cm

Question 5 :

Two vertical poles of heights 6 m and 3 m are erected above a horizontal ground AC. Find the value of y.  After having gone through the stuff given above, we hope that the students would have understood, "Word Problems on Similarity of Triangle".

Apart from the stuff given in this section "Word Problems on Similarity of Triangle"if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments... WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6