Exercise 24 Page 518

We want to find the length CP. Let's analyze the given rhombus.

We are given the lengths AB= 15 and PB=12. Note that sides in a rhombus are congruent and therefore have the same length. With this information, we can find the length of BC. AB= BC ⇔ BC= 15 Moreover, the diagonals are perpendicular. This means that △ CPB is a right triangle with legs CP and PB, and hypotenuse BC. We can use the Pythagorean Theorem to calculate CP. CP^2+PB^2=BC^2 ⇕ CP^2+12^2=15^2 Let's solve the equation.

CP^2+12^2=15^2

CalcPow

Calculate power

CP^2+144=225

SubEqn

LHS-144=RHS-144

CP^2=81

SqrtEqn

sqrt(LHS)=sqrt(RHS)

CP=9

Note that when solving the equation we kept the principal root. This is because CP is a side length, and must be positive. We found that CP=9.