Isosceles trapezoid ABCD is shown with midsegment EF. If base BC = 17x, base AD = 30x + 12, and EF = 22.5x + 9, what is BC?

Link to photo: https://cdn.flvs.net/assessment_images/educator_geometry_v22/02_06_28_flvs.gif

34
51
68
85

Question

Isosceles trapezoid ABCD is shown with midsegment EF. If base BC = 17x, base AD = 30x + 12, and EF = 22.5x + 9, what is BC?

Link to photo: https://cdn.flvs.net/assessment_images/educator_geometry_v22/02_06_28_flvs.gif

34
 51
 68
 85

Axolotl · Answer

@jhonyy9

jhonyy9 · Answer

EF is midsegment so what mean this ?

Axolotl · Answer

@jhonyy9 wrote:

EF is midsegment so what mean this ?

EF = BC EF = AD

jhonyy9 · Answer

not really 
look please on this image

jhonyy9 · Answer

isoscele trapezoid what mean ?

Axolotl · Answer

@jhonyy9 wrote:

not really look please on this image

It splits the isosceles trapezoid in half..

jhonyy9 · Answer

yes the lateral sides

but how are these lateral sides in case of an isoscele trapezoid ?

Axolotl · Answer

@jhonyy9 wrote:

yes the lateral sides but how are these lateral sides in case of an isoscele trapezoid ?

They are congruent?

jhonyy9 · Answer

|dw:1665092336205:dw|

jhonyy9 · Answer

BC = 17x
AD = 30x +12 
EF = 22,5x +9

BC = ?

Axolotl · Answer

@jhonyy9 wrote:

BC = 17x AD = 30x +12 EF = 22,5x +9 BC = ?

ermmm

jhonyy9 · Answer

so bc. the EF is a midsegment you can write

EF = (BC +AD ) / 2

and now from this expression you need calcule the x value

Axolotl · Answer

22.5x + 9 = (17x + 30x +12 ) / 2

jhonyy9 · Answer

exactly and from this x = ?

jhonyy9 · Answer

so to eliminate the denominator multiply both sides by 2

Axolotl · Answer

uhhhh so 22.5x + 9 times 2 and 17x + 30x +12  times 2?

Axolotl · Answer

I'm a bit confused

jhonyy9 · Answer

yes

2(22,5x +9) = 2(47x +12) /2

Axolotl · Answer

45x + 18 = 94x + 24 ?

jhonyy9 · Answer

not really

on the right side there is a denominator of 2 so the 2 with numerator and the 2 from denominator what will make ?

Axolotl · Answer

45x + 18 = 94x + 24 / 2 ?

Axolotl · Answer

I forgot about that part

jhonyy9 · Answer

not really bc. the 2 from top and bottom will simplify

jhonyy9 · Answer

@jhonyy9 wrote:

yes 2(22,5x +9) = 2(47x +12) /2

here on the right side 2 from numerator will be simplified by 2 from denominator

Axolotl · Answer

sooo

Axolotl · Answer

I'm still confused sorry :(

jhonyy9 · Answer

on the right side there is a fraction

to eliminate the denominator of this fraction just you need multiply the both sides by this number from denominator so

multiplie the left side by 2 in this case and multiplie the right side by 2 and in this way 2 from numerator and 2 from denominator will be simplified

and will get

45x +18 = 47x +12

x = ?

jhonyy9 · Answer

like a first step subtract from both sides 45x so what will get ?

Axolotl · Answer

@jhonyy9 wrote:

on the right side there is a fraction to eliminate the denominator of this fraction just you need multiply the both sides by this number from denominator so multiplie the left side by 2 in this case and multiplie the right side by 2 and in this way 2 from numerator and 2 from denominator will be simplified and will get 45x +18 = 47x +12 x = ?

oh ok

Axolotl · Answer

I got 3

jhonyy9 · Answer

for x = 3 BC = ?

Axolotl · Answer

@jhonyy9 wrote:

for x = 3 BC = ?

uhhhhh

jhonyy9 · Answer

BC = 17x

x = 3

BC = ?

Axolotl · Answer

Do i do 17x + 3?

jhonyy9 · Answer

no

BC = 17x

x = 3

BC = 17*3 = ?

Axolotl · Answer

@jhonyy9 wrote:

no BC = 17x x = 3 BC = 17*3 = ?

oh, 17 times 3 is 51

jhonyy9 · Answer

yes of cours

but now you need check it if x=3 is right

Axolotl · Answer

@jhonyy9 wrote:

yes of cours but now you need check it if x=3 is right

how do I do that for this question?

jhonyy9 · Answer

@axolotl wrote:

22.5x + 9 = (17x + 30x +12 ) / 2

start from here

Axolotl · Answer

22.5(3) + 9 = (17(3) + 30(3) +12 ) / 2

jhonyy9 · Answer

yes and now make the calcule to check if the left side will get equal right side

Axolotl · Answer

76.5 for the left side I think

jhonyy9 · Answer

no

jhonyy9 · Answer

3*22 = ?

Axolotl · Answer

66

jhonyy9 · Answer

3*0,5 = ?

Axolotl · Answer

1.5?

jhonyy9 · Answer

yes and now 66+1,5 = ?

Axolotl · Answer

67.5

jhonyy9 · Answer

yes of cours so not is 76,5 how you wrote it above

yes ?

Axolotl · Answer

@jhonyy9 wrote:

yes of cours so not is 76,5 how you wrote it above yes ?

yah

jhonyy9 · Answer

@axolotl wrote:

22.5(3) + 9 = (17(3) + 30(3) +12 ) / 2

67,5 = ? on the right side what will get ?

jhonyy9 · Answer

17*3 = ?

Axolotl · Answer

51

jhonyy9 · Answer

30*3 = ?

Axolotl · Answer

90

jhonyy9 · Answer

51+90+12 = ?

Axolotl · Answer

153

jhonyy9 · Answer

153/2 = ?

Axolotl · Answer

76.5!! 0o0

Axolotl · Answer

OMG thank you SOSO SO SO SO SO much! Words can't explain how grateful I am! I am so sorry I was a pain! This took us a whole hour :(

jhonyy9 · Answer

@axolotl wrote:

67.5

sorry we have forgot adding here again the 9 so you was right with 76,5

Axolotl · Answer

@jhonyy9 wrote:

@axolotl wrote:

67.5

sorry we have forgot adding here again the 9 so you was right with 76,5

It's fine

Axolotl · Answer

Thank you <3

jhonyy9 · Answer

so do you see it now the right side ot 76,5 is equal with left side of 76,5 what mean that x = 3 is correct - right value of x

Axolotl · Answer

@jhonyy9 wrote:

so do you see it now the right side ot 76,5 is equal with left side of 76,5 what mean that x = 3 is correct - right value of x

Yes. Thank you so much! I needed this!

jhonyy9 · Answer

np

anytime

cya

Axolotl · Answer

@axolotl wrote:

@jhonyy9 wrote:

so do you see it now the right side ot 76,5 is equal with left side of 76,5 what mean that x = 3 is correct - right value of x

Yes. Thank you so much! I needed this!

I'm sorry this took us a whole hour

jhonyy9 · Answer

np i m here happy to give help

cya

Axolotl · Answer

@jhonyy9 wrote:

np i m here happy to give help cya

If could give one billions medals, I would!

jhonyy9 · Answer

np

tysm

Axolotl · Answer

@jhonyy9 wrote:

np tysm

Your welcome! Have a great day!