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# OK Brilliant People

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Can this Geometry question be solve with the information given?. It was posted a day or so ago:

What is the area of an isosceles trapezoid with diagonals of length 17, all integer side lengths, and a perimeter of 50?

Oct 29, 2019

### 10+0 Answers

#1
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What is the area of an isosceles trapezoid with diagonals of length 17, all integer side lengths, and a perimeter of 50?

If the diagonals are the same length then it might be a rectangle.

length + breadth =25

\(l^2+b^2=17^2\\ (l+b)^2-2lb=289\\ (25)^2-2lb=289\\ 625-2lb=289\\ -2bl=-336\\ bl=168\)

The area is 168 units squared.     WRONG

I just checked and found that this answer cannot work. It cannot be a rectangle.

Oct 29, 2019
edited by Melody  Oct 29, 2019
#2
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Meoldy: Please look at this picture and see if it is the same. Thanks.

https://www.geogebra.org/m/xqV35GDP

Oct 29, 2019
#3
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Mmm, your right, Mine is just one possible answer, with regards to the diagonal lengths, and it certainly does not need to be a rectangle.

Plus I failed to account for the fact that all side lengths are integer.

So in short, mine is wrong.

Did you draw that pic or was it given to you?

Oct 29, 2019
edited by Melody  Oct 29, 2019
#4
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I just found it on the Internet.

Oct 29, 2019
#5
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I have drawn something similar.

The 17 is exact but the 50 is not.

I drew it in Geobebra and it has variables on a slider so the shape can be changed.

I actually do not think it should be that difficult to answer properly but I have not been sucessful

https://www.geogebra.org/classic/v4uveaev

Oct 29, 2019
#6
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I see you CPhill answering this question:

Let us see if you agree with I got!!.

Longer side (a):    21

Shorter side (b):   9

Legs (c):                10

Diagonal (d):       17

Height (h)             8

Central mediam:   15

Circumcircle radius (rc): 10.625

Overlap (g):               6

Perimeter (p):           50

Area (A):                    120

Acute angle (α):       53.13

Obtuse angle (β):    126.87

Oct 29, 2019
#7
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Thanks guest.

Here is the pic.

Did you get some program to work that out?

Here is the link to the actual geogebra build.    https://www.geogebra.org/classic/v4uveaev

Oct 30, 2019
edited by Melody  Oct 30, 2019
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Thanks Melody. I most certainly did by using this very nice calculator that solves "trapezoids":

https://rechneronline.de/pi/isosceles-trapezoid.php

Oct 30, 2019
#9
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Thanks, I will add that calc link to our reference material thread, found in our sticky topics.

Melody  Oct 30, 2019
#10
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Are you the same person who posted the question?

Melody  Oct 30, 2019