The perimeter of a trapezoid is 39a--‐7. Three sides have the following lengths: 9a, 5a +1, and 17a --‐6. What is the length of the fourth side? GIVING MEDALS AND WILL BECOME A FAN IF YOU'RE RIGHT! SHOW WORK.

Question

563blackghost · Answer

Remember 
$$P=a+b+c+d $$
 so we will have to work backwards so lets input what we know 
 $$39a−7=(9a)+(5a+1)+(17a−6) + (d) $$

563blackghost · Answer

so what should we do?

anonymous · Answer

Ww should add the numbers with the same variables?

563blackghost · Answer

Correct! so we will factor $$(9a)+(5a+1)+(17a-6)$$ now we are first going to group "like terms" so
$$(17a + 9a + 5a) + (1-6)$$

563blackghost · Answer

so whats the simplified equation?

anonymous · Answer

31a - 5?

563blackghost · Answer

Correct! now what do we do?

anonymous · Answer

Isnt
 that the answer?

anonymous · Answer

So then that equals 8a + 12?

563blackghost · Answer

not exactly. that is the sum of a,b and c. So we will have to subtract the perimeter with the sum of the sides. so...
$$(39−7)−(31a−5) $$
 but like last time we have to group "like terms" 
$$(39a−31a)−(−7+5)  $$

563blackghost · Answer

meant to put +5 sorry

563blackghost · Answer

so the answer will be 8a -2.

anonymous · Answer

Youre good, but ohh okay I see what I did wrong now

563blackghost · Answer

you can use Mathway.com for these kiinds of problems it helps really well.

anonymous · Answer

I tried that but I dont really want to pay to see how to do a problem, but thankyou!

563blackghost · Answer

anytime xD