Point b is between A and C. if AB =2x, BC =3x+1, and AC=21, find the length of BC

Question

asked Oct 2, 2023 157k views

2 Answers

Jfsantos · Answer 1 · 2023-10-08T09:50:08+0000

Explanation:

We are here given that a point B is between A and C . Also ,

And we would like to calculate the length of BC . For figure refer to the attachment. From figure we can see that ,

$\rm:\implies AC = AB + BC$

Substitute the respective values,

$\rm:\implies 21 = 2x + 3x + 1$

Add like terms ,

$\rm:\implies 21 = 5x +1$

Subtract 1 on both sides,

$\rm:\implies 21-1 = 5x$

Simplify,

$\rm:\implies 20=5x$

Divide both sides by 5,

$\rm:\implies \blue{ x = 4}$

Now consider ,

$\rm:\implies BC = 3x+1$

Plug in the value of x found above ,

$\rm:\implies BC= 3(4)+1$

Simplify,

$\rm:\implies BC = 12+1$

Add,

$\rm:\implies \underline{\boxed{\blue{\rm{ \quad BC \quad =\quad 13\quad }}}}$

And we are done !