Question

If ΔAOB ~ ΔCOD, and DO = 3x - 19, OB = x - 5, OC = x - 3 and AO = 3, then the value of x can be     ​

Answer 1

$\large\underline{\sf{Given- }}$

ΔAOB ~ ΔCOD and

• DO = 3x - 19

• OB = x - 5

• OC = x - 3

• AO = 3

$\large\underline{\sf{To\:Find - }}$

The value of x

$\large\underline{\sf{Solution-}}$

It is given that

• ΔAOB ~ ΔCOD

• DO = 3x - 19

• OB = x - 5

• OC = x - 3

• AO = 3

As it is given that, ΔAOB ~ ΔCOD

By Corresponding parts of Similar triangles, we have

$\rm :\longmapsto\:\dfrac{AO}{CO} = \dfrac{OB}{OD}$

$\rm :\longmapsto\:\dfrac{3}{x - 3}\rm \:  =  \: \dfrac{x - 5}{3x - 19}$

$\rm :\longmapsto\:9x - 57 = (x - 5)(x - 3)$

$\rm :\longmapsto\:9x - 57 = {x}^{2} - 5x - 3x + 15$

$\rm :\longmapsto\:9x - 57 = {x}^{2} - 8x+ 15$

$\rm :\longmapsto\:{x}^{2} - 17x+ 72 = 0$

$\rm :\longmapsto\:{x}^{2} - 9x - 8x+ 72 = 0$

$\rm :\longmapsto\:x(x - 9) - 8(x - 9) = 0$

$\rm :\longmapsto\:(x - 9)(x - 8) = 0$

$\bf\implies \:x = 9 \: \: or \: \: x = 8$

More to know :-

1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem :-

If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.

Answer 2

Answer:

Given−

ΔAOB ~ ΔCOD and

DO = 3x - 19

OB = x - 5

OC = x - 3

AO = 3

\large\underline{\sf{To\:Find - }}

ToFind−

The value of x

\large\underline{\sf{Solution-}}

Solution−

It is given that

ΔAOB ~ ΔCOD

DO = 3x - 19

OB = x - 5

OC = x - 3

AO = 3

As it is given that, ΔAOB ~ ΔCOD

By Corresponding parts of Similar triangles, we have

\rm :\longmapsto\:\dfrac{AO}{CO} = \dfrac{OB}{OD}:⟼

CO

AO

=

OD

OB

\rm :\longmapsto\:\dfrac{3}{x - 3}\rm \: = \: \dfrac{x - 5}{3x - 19}:⟼

x−3

3

=

3x−19

x−5

\rm :\longmapsto\:9x - 57 = (x - 5)(x - 3):⟼9x−57=(x−5)(x−3)

\rm :\longmapsto\:9x - 57 = {x}^{2} - 5x - 3x + 15:⟼9x−57=x

2

−5x−3x+15

\rm :\longmapsto\:9x - 57 = {x}^{2} - 8x+ 15:⟼9x−57=x

2

−8x+15

\rm :\longmapsto\:{x}^{2} - 17x+ 72 = 0:⟼x

2

−17x+72=0

\rm :\longmapsto\:{x}^{2} - 9x - 8x+ 72 = 0:⟼x

2

−9x−8x+72=0

\rm :\longmapsto\:x(x - 9) - 8(x - 9) = 0:⟼x(x−9)−8(x−9)=0

\rm :\longmapsto\:(x - 9)(x - 8) = 0:⟼(x−9)(x−8)=0

\bf\implies \:x = 9 \: \: or \: \: x = 8⟹x=9orx=8

More to know :-

1. Pythagoras Theorem :-

This theorem states that : In a right-angled triangle, the square of the longest side is equal to sum of the squares of remaining sides.

2. Converse of Pythagoras Theorem :-

This theorem states that : If the square of the longest side is equal to sum of the squares of remaining two sides, angle opposite to longest side is right angle.

3. Area Ratio Theorem :-

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

4. Basic Proportionality Theorem :-

If a line is drawn parallel to one side of a triangle, intersects the other two lines in distinct points, then the other two sides are divided in the same ratio.