Exercise 22 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 a mean of 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 measures of two bases of the trapezoid, and we're asked to find the width of the shelf that will be in the middle of a window box. To do this, we can use above formula. To find this length, let's substitute 22 and 12 for a and b into this formula.

x=1/2(a+b)

SubstituteII

a= 22, b= 12

x=1/2( 22+ 12)

AddTerms

Add terms

x=1/2(34)

MoveRightFacToNum

a/c* b = a* b/c

x=34/2

CalcQuot

Calculate quotient

x=17

She should make the shelf 17 inches wide.