In quadrilateral ABCD, we have AB = BC = CD = DA, AC = 14, and BD = 48. Find the perimeter of ABCD.
4 answers
A quadrilateral with all four sides equal is a rhombus, whose area is half the product of the diagonals AC and BD.
Yeah, but we're not trying to find the area?
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 each side of the rhombus, then
s²=(AC/2)²+(BD/2)²
using Pythagoras theorem.
Calculate
s=√(7²+24²)
=25
The perimeter is 4s.
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 each side of the rhombus, then
s²=(AC/2)²+(BD/2)²
using Pythagoras theorem.
Calculate
s=√(7²+24²)
=25
The perimeter is 4s.
Stop cheating Sheenybeany!
3 answers