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# Quadrilateral P is a rhombus.

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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??

Dec 19, 2020

#1
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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.

Dec 19, 2020
#2
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Thank you very much!!

Guest Dec 20, 2020
#3
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You're very welcome!

Guest Dec 20, 2020