Question

Rectangle ADEF and isosceles trapezoid FBCE both have a base of 15. The lower base angles of the trapezoid are 45° and the legs of the trapezoid are 8. How long is BC? Round your answer to the nearest tenth.

2.8
3.7
4.1
5.2

Answer 1

.

Answer 2

can you draw it ?

Answer 3

yea one sec

Answer 4

draw a perpendicular on FE from B
than us cos 45 to calculi this part of FE
so what you get hence multiplie by 2 and the result subtract from 15 and what will get will be the lenght of BC

hope so much that you understand right what i have wrote here

ok ?

Answer 5

thanks a bunch :)

Answer 6

do you know the value of cos 45 ?

Answer 7

so than this mean that you have got it easy ?

Answer 8

0.707 is the value of cos 45 right?

Answer 9

@jhonyy9 is 0.707 right?

Answer 10

you ther @jhonyy9

Answer 11

@seiga i dont get it :/

Answer 12

wait..

Answer 13

lol u know i aint good @ math, maybe @mathaddict4471 @mathgeek! @mathavraj can solve this, wait.

Answer 14

@mathaddict4471 @mathgeek! @mathaddict4471 @mathgeek898

Answer 15

@ZeHanz

Answer 16

@amistre64

Answer 17

can anyone solve this?:/

Answer 18

okay ley me see i took this math 2 years ago

Answer 19

aperently my math is too hard lol @seiga

Answer 20

lol no its not lol i just dont wanna give u the wrong answer lol shutup!

Answer 21

lol i get that you make a triangle but i put 45 in my calculator then hit cos but it gave me 0.707 and i know this aint the answer

Answer 22

lol im done talking to u, apparently im not smart enough-___-

Answer 23

If I've visualized this correctly, we can imagine perpendiculars from B and C to EF which divide the trapezoid into three parts: two 45° right triangles with hypotenuse 8 and a rectangle. From this we see that subtracting two legs of the triangles from the length of EF (given as 15) will give us the length of the side of the rectangle opposite BC, which is also the length of BC.

Let a be the side length of the right triangles. Then
a^2 + a^2 = 2a^2 = 8^2 = 64
a^2 = 32
a = √ 32 = 4√2
and
BC = 15 - 2(4√2) = 15 - 8√2 = about 3.7 (answer B).

Answer 24

@seiga your as smart as i need <3

Answer 25

lol do u get it now!

Answer 26

yes :) thanks @seiga

Answer 27

i read it so i know how to do this kind of question in the future :)

Answer 28

and yes you did :) <3

Answer 29

awww ty for the medal @seiga

Answer 30

so cos45 = (sqrt2)/2

i have thought that you have learned it ,sorry

Answer 31

Although you've already got an answer, I will try to give you an alternative one.
Both triangles ABF and CDE are special ones: 45-45-90 triangles.
What is so special about them?
They are half a square.
In a square, the length of a diagonal is √2 times bigger than the length of a side (this could be verified with the Pythagorean Theorem).

In ABF and CDE, the "diagonal" has length 8.
This is √2 times as long as AB or CD (or AF or DE).
So to get AB and CD, you have to divide 8 by √2.
Now:

\(BC=15 - AB - CD = 15 - 8/√2 - 8/√2 \approx\) (grabbing calculator...) \(3.7\), which is answer B (you already knew that).

Answer 32

@ZeHanz i figured it out, but i like ur describing it better(:

Answer 33

@seiga: Thank you, I consider this as a medal :D

Answer 34

lol , (: and can u figure out the question i tagged u in?(:pleasE!