**Example 1 :**

Find the unknown values of the following figure. All lengths are given in centimeters (all measures are not in scale)

EFCD is a parallelogram, So EF = 7 cm, DE = CF = 6 cm

**Solution :**

By considering triangles ∆ AEF and ∆ ABC,

∠AEF = ∠ABC (Corresponding angles)

∠A = ∠A (common angle)

By using AA similarity criterion ∆ AEF ~ ∆ ABC

(AF/AC) = (EF/BC)

[x/(x + 6)] = (7/12)

12x = 7 (x + 6)

12x = 7x + 42

12x - 7x = 42

5x = 42

x = 42/5

x = 8.4 cm

Considering the triangles ∆ BDG and ∆ BCF

(BD/BC) = (DG/CF)

DG = (BD/BC) ⋅ CF

y = (5/12)** **⋅ 6

y = 30/12

= 2.5 cm

**Example 2 :**

The image of the man of height 1.8 m, is length 1.5 cm on the film of a camera. If the film is 3 cm from the lens of the camera, how far is the man from the camera?

**Solution :**

Here AB represents height of man

CD represents height of reflection

Let “L” be the position of lens

LM represents distance between man and lens

LN represents distance between lens and tape.

Also the sides AB is parallel to the side CD, AB = 1.8 m. CD = 1.5 m, LN = 3 cm

From triangles ∆ LAB and ∆ LCD, we get

∠LAB = ∠LCD (alternate angles)

∠BLA = ∠DLC (vertically opposite angles)

By using AA similarity criterion ∆ LAB ~ ∆ LCD

(AB/CD) = (LM/LN)

(180/1.5) = (LM/3)

LM = (180 **x** 3)/1.5

LM = 360 cm

100 cm = 1 m

LM = 360/100

LM = 3.6 m

So the distance between man and camera is 3.6 m

**Example 3 :**

A girl of height 12 cm is walking away from the base of a lamp post at a speed of 0.6 m/sec . If the lamp is 3.6 m above the ground level, then find the length of her shadow after 4 seconds.

**Solution :**

Let AB be the height of lamp. CD be the height of girl and CE be the length of shadow of the girl.

AB = 3.6 m, CD = 120 cm ==> 1.2 m

The girl is walking at the rate of 0.6 m/sec. Now we are going to find the distance traveled by the girl

AC = 4(0.6) ==> 2.4 m

From the triangles ECD and EAB the sides CD is parallel to AB.

∠ECD = ∠EAB (corresponding angles)

∠E = ∠E (common angles)

By using AA similarity criterion ∆ ECD ~ ∆ EAB

(EC/EA) = (CD/AB)

[EC/(2.4 + EC)] = 1.2/3.6

[EC/(2.4 + EC)] = 1/3

3 EC = 1 (2.4 + EC)

3 EC = 2.4 + EC

3 EC – EC = 2.4

2 EC = 2.4

EC = 2.4/2

EC = 1.2 m

So length of shadow of the girl is 1.2 m.

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

HTML Comment Box is loading comments...

You can also visit the 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**