Question

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

Answer 1

+ BC = AC

x + 2x+1 = 22

3x +1 = 22

3x = 21

x = 7

AB = 7

BC = 2*7+1 = 14 + 1 = 15

15 - 2

13

Answer 2

Explanation:

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

• Value of AB = 2x
• Value of BC = 3x + 1
• Value of AC = 21 .

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 !