Exercise 36 Page 534

Let's analyze the given rhombus.

For all rhombi, the diagonals bisect each other. Therefore, DE and EB are equal. We already know that EB = 9. This means that DE is also 9. DE = EB ⇒ DE = 9 From the definition of rhombus we know that it has four congruent sides. Therefore, AB and CD are equal. Since we know that AB = 12, the length of DC is also 12. CD = AB ⇒ CD = 12 Finally, note that △ CDE is a right triangle. To find CE we can use the Pythagorean Theorem. DE^2 + CE^2 = CD^2 We already know that DE = 9 and CD = 12. Let's substitute these values into the above equation and solve for CD.

DE^2 + CD^2 = CE^2

SubstituteII

DE= 9, CD= 12

9^2 + CE^2 = 12^2

CalcPow

Calculate power

81 + CE^2 = 144

SubEqn

LHS-81=RHS-81

CE^2 = 63

SqrtEqn

sqrt(LHS)=sqrt(RHS)

CE = sqrt(63)

▼

Simplify

SplitIntoFactors

Split into factors

CE = sqrt(9(7))

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

CE = 3sqrt(7)

When solving the equation, we only considered the principal root because CE is the length of a segment and therefore must be positive.