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bulgar [2K]
3 years ago
14

In the kite , AK=9 , JK=15 , and AM=16 .

Mathematics
1 answer:
Veronika [31]3 years ago
4 0

Answer:

The Length of JM is 20.

Step-by-step explanation:

Given,

JKLM is a kite in which JL and KM are the diagonals that intersect at point A.

Length of AK = 9    

Length of JK = 15  

Length of AM = 16

Solution,

Since JKLM is a kite. And JL and KM are the diagonals.

And we know that the diagonals of a kite perpendicularly bisects each other.

So, JL ⊥ KM.

Therefore ΔJAK is aright angled triangle.

Now according to Pythagoras Theorem which states that;

"The square of the hypotenuse is equal to the sum of the square of base and square of perpendicular".

JK^2=KA^2+AJ^2

On putting the values, we get;

(15)^2=9^2+AJ^2\\\\225=81+AJ^2\\\\AJ^2=225-81=144

On taking square root onboth side, we get;

\sqrt{AJ^2} =\sqrt{144}\\\\AJ=12

Again By Pythagoras Theorem,

AJ^2+AM^2=JM^2

On putting the values, we get;

JM^2=(12)^2+(16)^2\\\\JM^2=144+256=400

On taking square root onboth side, we get;

\sqrt {JM^2}=\sqrt{400}\\\\JM=20

Hence The Length of JM is 20.

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