Given: △acm, m∠c=90°, cp ⊥ am , ac: cm=3: 4, mp-ap=1. find am.

AM = 25/7

Step-by-step explanation:

Lets say that PM = x

Then AP = x-1

They are in the scale of 3:4, so

CP = 3/4 *x or 3x/4

CP also equals 4/3 *(x-1) or 4x-4/3

That means that

4x-4  = 3x

 3         4

Then just do some cross multiplication to get

16x-16 = 9x

Then subtract and get 7x = 16, or

x = 16/7

Then substitute x in and get AM = 32/7 - 7/7 or

AM = 25/7

Step-by-step explanation:

Given that ACM is a right angled triangle.

Angle C =90 and also angle P =90

AC:CM=3:4

... i

Let AC=3k and CM=4k

Then by pythagorean theorem

From i, we get

Triangles APC and ACM are similar, since

angle A is common and one angle is right angle

AP/AC = AC/AM (Since triangles are similar)