Find AB if AC = 17, BC = 2x – 3, and AB = 3x. A) 12 C) 10 B) 18 D) 3
1 answer:
Answer:
A) 12
You know:
<em>AB= 3x</em>
<em>AB= 3xAC= 17</em>
<em>AB= 3xAC= 17BC= 2x-3</em>
Therefore, you can put the values in a number line for reference. By doing this you can see that <em>3x + 2x -3</em> (or AB +BC) <em>= 17</em> (or AC)
From here you can set up the equation to be:
<em>1</em><em>7</em><em> </em><em>=</em><em> </em><em>2</em><em>x</em><em> </em><em>-</em><em> </em><em>3</em><em> </em><em>+</em><em> </em><em>3</em><em>x</em>
and solve for x by combining like terms:
<em>1</em><em>7</em><em>=</em><em> </em><em>5</em><em>x</em><em>-</em><em>3</em>
adding 3 to both sides:
<em>2</em><em>0</em><em>=</em><em>5</em><em>x</em>
dividing each side by 5:
<em>20/5=5x/5</em>
to get:
<em>x=4</em>
then, you're gonna plug in your <em>x</em> (4) into <em>3x</em> (your AB) in order to solve for AB:
<em>AB=3x</em>
<em>AB=3x =3(4)</em>
<em>AB=3x =3(4) =12</em>
therefore, your answer is:
AB = 12
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