Question

Triangle ABC is similar to triangle DEF. The following ratios of corresponding sides are equal
8/12=16/24=(4x+5)/(4x+11)

Answer 1

x= ?

Answer 2

Ok! Hello again! So we know that the ratio that we need is 8/12 (or 2/3) right?

\[\frac{4x+5}{4x+11}=\frac{2}{3}\]

Answer 3

ok yes

Answer 4

Now we just solve for x. So multiply bit sides by \(4x+11\) gives what?

Answer 5

8x/3+22/3 thats just a guess im not exaclty sure

Answer 6

Well multiplying both sides by \(4x+11\) will cancel on the right hand side and will remain on the left. Something like\[4x+5 = \frac{2}{3}(4x+11)\]With me so far?

Answer 7

ok yes that makes more sense

Answer 8

Sorry so yes you are right, however it is worth not multiplying out until later.

Answer 9

Now we can multiply both sides by 3 giving: \[3(4x+5) = 2(4x+11)\]

Answer 10

Does that make sense so far?

Answer 11

to get rid of the fraction yes im with you

Answer 12

Brilliant, now we simply multiply through to remove the brackets and solve for x. \[12x+15 = 8x+22\]\[4x = 7\]\[x = \frac{4}{7}\]

Take a moment to make sure you understand these steps

Answer 13

when i put in 4/7 for the answer it said I was wrong

Answer 14

Oh sorry, I made a typo\[4x = 7\]\[x = \frac{7}{4}\] Hopefully you can see where I went wrong?

Answer 15

ok yes divide both sides by 4

Answer 16

We can check our answer by substituting that back in to our equation at the beginning.\[\frac{4x + 5}{4x +11}\]now sub in \(x = \frac{7}{4}\) giving\[\frac{4 \times \frac{7}{4} + 5}{4 \times \frac{7}{4} + 11}\]\[\frac{7+5}{7+11}=\frac{12}{18} = \frac{2}{3}\]Hurray! we have made sure our answer is right!

Answer 17

Let me know if you have any problems with that

Answer 18

ok thank you very much you're always a great help