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?

Guest Oct 29, 2019

#1**0 **

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. **

Melody Oct 29, 2019

#2**+1 **

Meoldy: Please look at this picture and see if it is the same. Thanks.

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

Guest Oct 29, 2019

#3**+1 **

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?

Melody Oct 29, 2019

#5**+1 **

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

Melody Oct 29, 2019

#6**+2 **

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

Guest Oct 29, 2019

#7**+2 **

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

Melody Oct 30, 2019