Exercise 9 Page 517

Let's analyze the given rhombus.

To find the length AC we must first find the value of x. By the Segment Addition Postulate, we can express the length of the diagonal AC as the sum of AP and PC. AC= AP+PCFor all rhombi, the diagonals bisect each other. Therefore, the lengths of AP=3x-1 and PC=x+9 are equal. AP = PC ⇕ 3x-1 = x+9 Let's solve the equation.

3x-1=x+9

SubEqn

LHS-x=RHS-x

2x-1=9

AddEqn

LHS+1=RHS+1

2x=10

DivEqn

.LHS /2.=.RHS /2.

x=5

We found that x=5. Let's calculate the length of AC. AC=AP+PC ⇕ AC=3x-1+x+9 To do so, we will substitute the value x=5.

AC=3x-1+x+9

Substitute

x= 5

AC=3(5)-1+5+9

Multiply

Multiply

AC=15-1+5+9

AddSubTerms

Add and subtract terms

AC=28

We found that the length of AC is 28.