Asked by Sheenybeany

In quadrilateral ABCD, we have AB = BC = CD = DA, AC = 14, and BD = 48. Find the perimeter of ABCD.

Answers

Answered by MathMate
A quadrilateral with all four sides equal is a rhombus, whose area is <i>half</i> the product of the diagonals AC and BD.
Answered by Sheenybeany
Yeah, but we're not trying to find the area?
Answered by MathMate
Sorry.
In that case, we make use of the fact that rhombuses have diagonals which intersect at right-angles.
Thus each side is the hypotenuse of a right triangle with legs equal to the half-diagonals.

Thus if s=length of <i>each</i> side of the rhombus, then
s²=(AC/2)²+(BD/2)²
using Pythagoras theorem.
Calculate
s=√(7²+24²)
=25

The perimeter is 4s.
Answered by AoPS
Stop cheating Sheenybeany!
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