McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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Exercise 41 Page 534

19.2

Practice makes perfect

If a quadrilateral is a kite, then its diagonals are perpendicular. Let K be the point of intersection of the diagonals.

Notice that △ GHK is a right triangle. To find GH we will use the Pythagorean Theorem. GK^2 + KH^2 = GH^2 We already know that GK = 12 and KH = 15. Let's substitute these values into the above equation and solve for GH.
GK^2 + KH^2 = GH^2
12^2 + 15^2 = GH^2
144 + 225 = GH^2
369 = GH^2
GH^2 = 369
GH = sqrt(369)
GH=19.209372...
GH ≈ 19.2
Wehn solving the equation, we only considered the principal root. The reason for this is that GH is the length of a segment and therefore cannot be negative.