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Which value of x would make Line segment F G is parallel to line segment B C?

2 Answers

3 votes

Answer:

option 4, X=9

Explanation:

User Muilpp
by
8.0k points
2 votes

Answer:

x = 9

Explanation:

Consider the below figure attached with his question.

In the below figure
FA=x+1, FB=x+6, GA=x-1\text{ and }GC=x+3.

According to Basic Proportionality Theorem (BPT), if a line is parallel to one side of a triangle, then it divides the two remaining sides in the same ratio.

Using BPT theorem,


(FA)/(FB)=(GA)/(GC)


(x+1)/(x+6)=(x-1)/(x+3)

On cross multiplication we get


(x+1)(x+3)=(x-1)(x+6)


x^2+3x+x+3=x^2+6x-x-6


4x+3=5x-6


4x-5x=-6-3


-x=-9


x=9

Hence, FG║BC if the value of x is 9.

Which value of x would make Line segment F G is parallel to line segment B C?-example-1
User Xavierzhao
by
7.6k points