Exercise 56 Page 549

We are asked to find the length of segment AB in the given trapezoid.

Recall that if a quadrilateral is a trapezoid, then the length of the midsegment is half the sum of the lengths of the bases. ST= 1/2 (CD+AB) We can substitute the given lengths of these segments into this equation. 9=1/2 (( 3x+2)+( x+4)) Let's solve this equation to find x.

9=1/2((3x+2)+(x+4))

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Solve for x

RemovePar

Remove parentheses

9=1/2(3x+2+x+4)

AddTerms

Add terms

9=1/2(4x+6)

MultEqn

LHS * 2=RHS* 2

18=4x+6

SubEqn

LHS-6=RHS-6

12=4x

DivEqn

.LHS /4.=.RHS /4.

3=x

RearrangeEqn

Rearrange equation

x=3

Now that we found x, we can find AB by substituting x= 3 into the expression for its length, x+4. AB= 3+4 ⇕ AB=7