**Solving Word Problems in Similar Triangles :**

In this section, let us learn how to solve word problems in similar triangles.

**Example 1 :**

The
lengths of the three sides of triangle ABC are 6 cm, 4 cm and 9 cm. Triangle
PQR ad BC are congruent. One of the lengths of the sides of triangle PQR is 35
cm. What is the greatest perimeter possible for triangle PQR

**Solution :**

From the given information let us draw a rough diagram.

∆ PQR ~ ∆ ABC

PQ/AB = QR/BC = PR/AC = perimeter of ∆ PQR/Perimeter of ∆ BC

Let QR = 35

The corresponding sides must be QR and BC.

Perimeter of ∆ PQR/ Perimeter of ∆ ABC = QR/BC= 35/4

Perimeter of triangle PQR = (35/4) ⋅ 19

= 665/4

= 166.25

So, perimeter of triangle PQR is 166.25 cm².

**Example 2 :**

In the figure given below, the sides DE and BC are parallel and (AD/B) = 3/5, calculate the value of

(i) area of triangle ADE/are of triangle ABC

(ii) area of trapezium BCED/area of triangle ABC

**Solution :**

In triangle ABC, the sides DE and BC are parallel

Area of ∆ ADE/ Area of ∆ ABC = AD²/AB²

= (3k)²/(8k)²

= 9/64

(ii) Area of ∆ ADE = 9 k

Area of ∆ ADE = 64 k

Area of trapezium BCDE = area of ∆ ABC – area of ∆ ADE

= 64 k – 9 k

= 55 k

Area of trapezium BCDE/Area of ∆ ABC = 55 k/64 k

= 55/64

**Example 3 :**

The government plans to develop a new industrial zone in an unused portion of land in a city.

The shaded portion of the map shown given below indicates the area of the new industrial zone. Find the area of the new industrial zone.

**Solution :**

By considering the lines AD and BC,the angles

∠AEB = ∠DEC (vertically opposite angles)

∠ EAB = ∠EDC (alternate angles)

By using AA similarity criterion ∆ EAB ~ ∆ EDC

(AB/DC) = (EF/EG)

EF = (AB/DC) **x**
EG

= (3/1) **x** 1.4

= 4.2 km

Area of new industrial zone = Area of ∆ EAB

= (1/2) ⋅ AB ⋅ EF

= (1/2) ⋅ 3 ⋅ 4.2

= 6.3 km²

So the area of new industrial zone is 6.3 km²

After having gone through the stuff given above, we hope that the students would have understood, how to solve word problems in similar triangles.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Widget is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**