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Rhombus ABCD has perimeter 148, and one of its diagonals has length 24. How long is the other diagonal?

Guest Aug 26, 2018

Best Answer 

 #1
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First, find the length of a side. Since it is a rhombus, the side length is \(148/4=37\)

Applying the pythagorean theorem, we get half the diagonal squared plus half 24 squared equals the side length squared.

So \((\frac{1}{2}x)^2+12^2=37^2\) and half the diagonal is equal to \(35\)

Thus the diagonal is equal to \(35*2=70\)

Guest Aug 26, 2018
 #1
avatar
+1
Best Answer

First, find the length of a side. Since it is a rhombus, the side length is \(148/4=37\)

Applying the pythagorean theorem, we get half the diagonal squared plus half 24 squared equals the side length squared.

So \((\frac{1}{2}x)^2+12^2=37^2\) and half the diagonal is equal to \(35\)

Thus the diagonal is equal to \(35*2=70\)

Guest Aug 26, 2018
 #2
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Thanks!

Guest Aug 28, 2018

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