Question

In training ABC, points M and N lie on AB and AC respectively and MN||BC. If AM=x+1,MB =x, AN=3x-3 and NC=4x-10 then find x. ​

Answer 1

Answer:

We have MN || BC

•°• ∆AMN ~ ∆ ABC (C P C T)

then, AM/BM = AN/NC (BY BASIC PROPORTIONALITY THEOREM)

x+1/x = 3x-3/4x-10 .......,.......................(I).

then we take cross multiplication.

x(3x-3)= (x+1) (4x-10)

3x2 -3x = x(4x-10) +1(4x-10)

3x2 -3x = 4x2 -10x +4x -10

10x+10-4x-3x = 4x2 -3x2

10x-7x+10 = X2

3x+10 = X2

-x2+3x+10

Then we take Middle term splitting

-x2+3x+10=0

-x2+5x-2x+10=0

-x(x-5)-2(x-5)

(-x-2)(x-5)...

(-x-2)=0, -x=2,. •°• x=-2

(x-5) =0, •°• x=5

we take positive integer only.

we take x=5 .

•°•AM= x+1 = 5+1=6

MB=x=5

AN=3x-3=12

NC=4x-10=10.

This is the answer

If we have to prove the value of X then we put in equation (I)

Thanq you.