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??

Guest Dec 19, 2020

#1**0 **

Area of a kite A = (12 * 20) / 2 = 120 u^{2}

The diagonals of a rhombus divide its area into 4 congruent right-angled triangles. Since the area of the whole rhombus is 120 u^{2}, the area of a single triangle is 30 u^{2}. In order to find sides of this triangle, we can double its area.

1st attempt: 6 * 10 = 60 sqrt(6^{2} + 10^{2}) = 11.662 no good

2nd attempt: 5 * 12 = 60 sqrt(5^{2} + 12^{2}) = 13 **good **

So, the length of a side of quadrilateral P is 13 units.

Guest Dec 19, 2020