B is a point in the line segment AC such that it lies between A and C if AB = 9cm and AB*AC=12(BC)^2

MUKESH KUMAR   10 years AGO

B is a point in the line segment AC such that it lies between A and C and AB = 9 cm
Let BC = x cm
⇒ AC = AB + BC = 9 cm + x cm = (9 + x) cm
also AB × AC = 12 (BC)2
⇒ 9(9 + x) = 12x 2
⇒ 3(9 + x) = 4x 2
⇒ 27 + 3x = 4x 2
⇒ 4x 2 - 3x - 27 = 0
⇒ 4x 2 - 12x + 9x - 27 = 0
⇒ 4x(x - 3) + 9(x - 3) = 0
⇒ (4x + 9)(x - 3) = 0
⇒ x = -9/4 , 3
Since length of BC cannot be negative
Thus, x = 3
Hence, the required length of BC is 3 cm

Like? Yes (14) | No (3)  

NIDHI   10 years AGO

if BC = x cm
AC = AB + BC = 9 cm + x cm = (9 + x) cm
and AB × AC = 12 (BC)2
9(9 + x) = 12x 2
3(9 + x) = 4x 2
27 + 3x = 4x 2
4x 2 - 3x - 27 = 0

⇒ x = -9/4 , 3

length of BC is 3 cm

Like? Yes (5) | No (2)  

Jigyasa Kumar   10 years AGO

ANSWER :3
let the length be L
then 9L = 12(L-9)^2
L=12
so, BC = 12-9 = 3

Like? Yes (3) | No (1)  

Aarush Singh   10 years AGO

let the total length be L
then, 9L=12(L-9)^2
L=12
so BC=12=9=3

Like? Yes (2) | No (1)  

praveen sb   10 years AGO

As B lies b/w A n C andthus put AC=AB+BC in given eqn ie AB.AC=12(BC)^2,by solving we get BC=3

Like? Yes (2) | No (1)  

dulal sarkar   10 years AGO

AB*AC=12*(BC)^2
AB(AB+BC)=12*BC^2
12*BC^2-AB*BC-AB^2=0
AGAIN AB=9 cm.SO
12*BC^2-9*BC-81=0
On solving by quadratic formula we get BC=3 cm.

Like? Yes (1) | No   

aniruddh shrivastava   10 years AGO

see, first of all we have AB+BC=AC,
so after putting the value of AB in given equation, we have....
AB*AC=12(BC)^2
=> 9AC = 12(BC)^2
=> (BC)^2 = 9/12(AC)
so we have to put the value of BC one by one from the given options....only 6th option is fulfilling the condition

Like? Yes (1) | No   

AMAR NATH   10 years AGO

AB*AC=12(BC)^2
9*(9+BC)=12(BC)^2
BC^2-9*BC-81=0
ON SOLVING THE EQUATION
BC=3,-9/4
IGNORE THE NEGATIVE VALUE

Like? Yes (1) | No   

Sachin Parikh   10 years AGO

We get a quadratic equation that is 4(bc)^2-3(bc)-27=0
on solving we get - 2.25 cm and 3 cm as the possible value for bc. length cant be in negative thus 3 cm is the correct ans

Like? Yes (1) | No   

Balakumaran N.A   10 years AGO

Let BC = x cm
⇒ AC = AB + BC = 9 cm + x cm = (9 + x) cm
also AB × AC = 12 (BC)2
⇒ 9(9 + x) = 12x 2
⇒ 3(9 + x) = 4x 2
⇒ 27 + 3x = 4x 2
⇒ 4x 2 - 3x - 27 = 0
⇒ 4x 2 - 12x + 9x - 27 = 0
⇒ 4x(x - 3) + 9(x - 3) = 0
⇒ (4x + 9)(x - 3) = 0
⇒ x = -9/4 , 3
Since length of BC cannot be negative
Thus, x = 3
Hence, the required length of BC is 3 cm

Like? Yes (1) | No   

Abhishek misra   10 years AGO

let the length of BC=xcm
9*(9+x)=12*x^2
3*(9+x)=4*x^2
4*x^2-3*x-27=0
4*x^2-12*x+9*x-27=0
4*x(x-3)+9*(x-3)=0
(x-3)*(4*x+9)=0
x-3=0
x=3
BC=3cm

Like? Yes (1) | No   

shekhar pankaj   10 years AGO

ab/bc=12*bc/ac
so 3/x=12/(9+x)
so solve it it is now quad eqn
roots will be 3 and -3/4... reject -ve answer
ans 3

Like? Yes (1) | No   

sameer singh   10 years AGO

12bc^2=81+9bc
4bc^2=27+3bc
4bc^2-3bc-27=0
bc=3+-(9+16*27)^1/2

Like? Yes (1) | No   

raksha agrawal   10 years AGO

let bc=x
then ab*ac=12(bc)62
will be
9*(9+x)=12*x^2

Solving this will get bc=x=3

Like? Yes (2) | No (2)  

Anil Kumar Bharti   10 years AGO

Exp:
let bc=x
AB = 9cm
AB*AC=12(BC)^2
9*(9+x)=12*x^2
after solving...
x=3 cm Ans

Like? Yes (1) | No (1)  

debabrata sarkar   10 years AGO

AB*AC=12*(BC)^2
AB(AB+BC)=12*BC^2
12*BC^2-AB*BC-AB^2=0
AGAIN AB=9 cm.SO
12*BC^2-9*BC-81=0
On solving by quadratic formula we get BC=3 cm.

Like? Yes (1) | No (1)  

Divakar PC   10 years AGO

Substituting value of AB in the given equation we get-
9*AC=12(BC)^2
Now AC=(AB+BC)
So,AC=(9+BC)
Now we can write the equation as-
9(9+BC)=12*BC^2
So now it becomes a quadratic equation which is-
12*BC^2-9*BC-81=0
Solving for BC we get-
BC=3 cm
The other solution of quadratic equation is a negative integer so we ignore it.

Like? Yes (1) | No (1)  

mohan lal garg   10 years AGO

let bc=x
9(9+x)=12x^2
4x^2-3x-27=0
(x-3)(4x+3)
so x=3

Like? Yes (3) | No (3)  

Swastika Chatterjee   10 years AGO

9(AB+BC)=12BC^2
12BC^2=9BC+81
4BC^2-3BC-81=0
BC=3

Like? Yes (1) | No (1)  

shivendra pratap singh   10 years AGO

AB*AC=12(BC)^2
let BC=x and AB=9(given)
9(9+x)=12*x^2
we get quadratic equation as
4*x^2-3*x-27 by solving this we get:
x=3=BC
so option 6)3 cm is correct option

Like? Yes (2) | No (2)  

vishwanand   10 years AGO

let bc=x
then ac==x+9
then put the values in the equation
then solve,
9(x+9)=12(x)^2.
we get values 3 and -9.
so three is taken as the answer.

Like? Yes (1) | No (2)  

vigneshwari   10 years AGO

Let BC be X cm.
Then AC = 9+X cm.
ABxAC = 12x BC^2 => 9(9+X) = 12xX^2
=> 81+9X = 12X^2
4X^2 - 3X - 27 = 0
Solving this quadratic eqn, we have X = 3.
Hence, BC = 3 cm.

Like? Yes (1) | No (2)  

shravya   10 years AGO

AB*AC=12*BC^2
9*(9+X)=12*X^2
X=3cm

Like? Yes (1) | No (3)