Question

Given ACM, angle C=90º. AP=9, PM=12. Find AC, CM, AM.

Answer 1

Answer:

AM = 25, AC = 15, CM = 20

Step-by-step explanation:

The given parameters are;

In ΔACM, ∠C = 90°, $\overline{CP}$ ⊥ $\overline{AM}$, AP = 9, and PM = 16

$\overline{AC}$² + $\overline{CM}$² = $\overline{AM}$²

$\overline{AM}$ = $\overline{AP}$ + PM = 9 + 16 = 25

$\overline{AM}$ = 25

$\overline{AC}$² = $\overline{AP}$² + $\overline{CP}$² = 9² +  $\overline{CP}$²

∴ $\overline{AC}$² = 9² +  $\overline{CP}$²

Similarly we get;

$\overline{CM}$² = 16² + $\overline{CP}$²

Therefore, we get;

$\overline{AC}$² + $\overline{CM}$² = 9² +  $\overline{CP}$² + 16² + $\overline{CP}$² = $\overline{AM}$² = 25²

2·$\overline{CP}$² = 25² - (9² + 16²) = 288

$\overline{CP}$² = 288/2 = 144

$\overline{CP}$ = √144 = 12

From $\overline{AC}$² = 9² +  $\overline{CP}$², we get

$\overline{AC}$ = √(9² +  12²) = 15

$\overline{AC}$ = 15

From, $\overline{CM}$² = 16² + $\overline{CP}$², we get;

$\overline{CM}$ = √(16² + 12²) = 20

$\overline{CM}$ = 20.