Question

Given: ΔACM, m∠C = 90º

Answer 1

Answer: Value of CP = 12 units

Value of CM = 20 units.

Step-by-step explanation:

Since we have given that

Given: ΔACM, and  m∠C = 90º and CP⊥ AM and

AC = 15  , AP = 9, PM = 16

Now, we need to find the value of CP and CM,

As we know the formula :

$PM=\frac{CM^2}{AM}\\\\16=\frac{CM^2}{16+9}\\\\16=\frac{CM^2}{25}\\\\16\times 25=CM^2\\\\\sqrt{16\times 25}=CM\\\\4\times 5=CM\\\\20=CM$

Similarly,

$CP=\frac{AC\times CM}{AM}\\\\CP=\frac{15\times 20}{25}\\\\CP=3\times 4\\\\CP=12$

Hence, Value of CP = 12 units

Value of CM = 20 units.

Answer 2

CP=12, CM=20. CP is the altitude of the triangle. ACP is a right triangle, so you can solve for CP using Pythagorean's theorem. CP=\sqrt(AC^2-CP^2)=\sqrt(15^2-9^2)=12. AM=AP+PM=9+16=25. Triangle ACM is another right triangle, and CM=\sqrt(AM^2-AC^2)=\sqrt(25^2-15^2)=20.