We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

1. We know Angle B=Angle C, BE=5, CE=4 If the area of AEB=50 what is the area of CED?

2. The area of square ABCD is 36. E is a point on line CD such that CE=2ED. The extensions of line AE and line BE intersect at F. Find the area of DEF.

3. In the diagram below, we have angle ABC=angle CAB=angle DEB=angle BDE. Given that AE=21 and ED=27, find BD.

4. In the diagram below, we have angle ABC=angle CAB=angle DEB=angle BDE. Given that AE=21 and ED=27, find CA.

Guest Oct 22, 2018

#1**+9 **

I'd love to answer these except for the fact that they're under moderation right now...It says that moderation is at 74%, then it goes back down to 8%, and so on. I've been seeing this on almost every graph I see here for the past two days...weird.

KnockOut Oct 22, 2018

#2**+1 **

....but apparently the moderators can see the submissions....cphil has answered several that still say 'waiting for moderator'

ElectricPavlov Oct 22, 2018

#3**+2 **

First one

Triangle AEB is similar to triangle DEC

Note that EC /EB = 4/5 so...this is the scale factor of triangle DEC to triangle AEB

So......the area of triangle DEC =

[ scale factor of triangle DEC to triangle AEB ]^ 2 * area of triangle AEB =

[ 4/5] ^2 * 50 =

[ 16 / 25 ] * 50 =

16 * 2 =

32

CPhill Oct 22, 2018

#5**+2 **

Second one

Because DC is parallel o AB, then triangle BAF is similar to triangle EDF

And since the side of the square = sqrt (36) = 6

Then DE + EC = 6

DE + 2DE = 6

3DE = 6

DE = 2

So

[AB ] / [AD + DF ] = DE / DF

6 / [ 6 + DF ] = 2 / [ DF ] cross-multiply

6 [ DF ] = 2 [ 6 + DF ]

6DF = 12 + 2DF subtract 2DF from both sides

4DF = 12 divide both sides by 4

DF = 3 = height of triangle DEF

So area of DEF = (1/2)DE * DF = (1/2) * 2 * 3 = 3 units^2

CPhill Oct 22, 2018