Exercise 24 Page 527

We want to find the length of YZ.

Recall that in a kite, we have two pairs of consecutive congruent sides. In this case, YX≅ YZ and WZ≅ WX. Let's add this information to the diagram.

If a quadrilateral is a kite, then its diagonals are perpendicular. Therefore, we know that the given segments are the legs of a right triangle. Therefore we can use the Pythagorean Theorem to write the following equation. 5^2+ 8^2= XY^2 Let's solve this equation using inverse operations.

5^2+8^2=XY^2

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Solve for XY

CalcPow

Calculate power

25+64=XY^2

AddTerms

Add terms

89=XY^2

RearrangeEqn

Rearrange equation

XY^2=89

SqrtEqn

sqrt(LHS)=sqrt(RHS)

XY=±sqrt(89)

XY > 0

XY=sqrt(89)

Since YX≅ YZ, it must be that YZ=sqrt(89).