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

Step-by-step explanation:

It is given that in △ACM, m∠C=90°, CP ⊥ AM

, AC:CM=3:4, MP-AP=1.

Let AC=3x and CM=4x, then from △ACM, we get

Now, AM=MP+AP⇒5x=MP+AP    (1)

It is also given that MP-AP=1         (2)

Therefore, from (1) and (2),

(MP+AP)(MP-AP)=5x

Add and subtract on the left side,

           (3)

But, since CP ⊥ AM, Δ CMP and Δ CAP are right triangles. Therefore,

and

Thus, Equation (3) becomes,

Therefore, AM=5x

.

your answer would be 12