Exercise 23 Page 527

Let's begin with recalling the Trapezoid Midsegment Theorem. This theorem tells us that if x is the midsegment of a trapezoid, then this midsegment is parallel to both bases of this figure, and x is the mean of the lengths of the bases of the trapezoid. Let's call the bases a and b. x=1/2(a+b) In our exercise, we are given the lengths of two keys that are bases of the drawn trapezoid. To find the length of the G key, which is the middle key in this xylophone, we can use the above formula. Let's substitute 6 and 1.8 for a and b into this formula and evaluate.

x=1/2(a+b)

SubstituteII

a= 6, b= 1.8

x=1/2( 6+ 1.8)

AddTerms

Add terms

x=1/2(7.8)

MoveRightFacToNum

a/c* b = a* b/c

x=7.8/2

CalcQuot

Calculate quotient

x=3.9

The G key has a length of 3.9 inches.