Question

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

What is JM ?

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Kite J K L M with shorter diagonal J L intersecting longer diagonal K M at point A.

Answer 1

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.