Quadrilateral P is a rhombus.
Where an angle between one diagonal and a side is x
Quadrilateral Q is a kite having diagonals of 20 cm and 12 cm.
Note: The diagonals intersect at 90 degrees and are unequal.
Now Quadrilateral P has the same area as Quadrilateral Q. The lengths of the diagonals and sides of quadrilateral P are all integer values.
Find the length of a side of Quadrilateral P.
Help pls asap; the answer says 13 but why??
Area of a kite A = (12 * 20) / 2 = 120 u2
The diagonals of a rhombus divide its area into 4 congruent right-angled triangles. Since the area of the whole rhombus is 120 u2, the area of a single triangle is 30 u2. In order to find sides of this triangle, we can double its area.
1st attempt: 6 * 10 = 60 sqrt(62 + 102) = 11.662 no good
2nd attempt: 5 * 12 = 60 sqrt(52 + 122) = 13 good
So, the length of a side of quadrilateral P is 13 units.