Charlene puts together two isosceles triangles so that they share a base, creating a kite. the legs of the triangles are 10 inches and 17 inches, respectively. if the length of the base for both triangles is 16 inches long, what is the length of the kite’s other diagonal?

Length of kite’s other diagonal is  21 inches

Charlene puts together two isosceles triangles so that they share a base to form a kite

Let Δ ABC and ΔDBC are two isosceles triangles.  

Leg of Δ ABC  = 10 inches

Leg of ΔDBC = 17 inches

Both have common base BC

Length of BC = 16

From the properties of isosceles triangle we can write that

The altitude of isosceles triangle bisects the base of the isosceles triangle.

From the figure attached we can write

Hence BP = PC = 8 inches

Length of diagonal AD is to be determined by equation (1)

AP +PD = AD .........(1)

From Pythagoras theorem we can write

Applying Pythagoras them we can find Length of AP and PD

Similarly

So from equation (1) length of diagonal AD= AP +PD = 15 +6 = 21 inches

hence length of kite’s other diagonal is  21 inches

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