Exercise 1 Page 537

We are asked to find the length of RS 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. RS= 1/2 (MN + PO) We can substitute the given lengths of these segments into this equation. 9x - 1=1/2 (( 10x+3)+( 4x + 7)) Let's solve this equation to find x.

9x - 1 = 1/2((10x + 3)+(4x + 7))

▼

Solve for x

RemovePar

Remove parentheses

9x - 1 = 1/2(10x + 3 + 4x + 7)

AddTerms

Add terms

9x - 1 = 1/2(14x + 10)

MultEqn

LHS * 2=RHS* 2

18x - 2 = 14x + 10

SubEqn

LHS-14x=RHS-14x

4x - 2 = 10

AddEqn

LHS+2=RHS+2

4x = 12

DivEqn

.LHS /4.=.RHS /4.

x = 3

Now that we found x, we can find RS by substituting x=3 into the given expression, 9x - 1. RS= 9(3) - 1 ⇔ RS = 26 This corresponds to option D.