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

find am.

Step-by-step explanation:

Given: △ACM, m∠C=90°, CP ⊥ AM , AC:CM=3:4, MP-AP=1.

Solution: Let AC=3k and CM=4k, then from △ACM, we get

Now, AM=MP+AP⇒5k=MP+AP    (1)

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

Therefore, from (1) and (2),

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

Add and subtract on left side

          (3)

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

Thus, Equation (3) becomes,

Thus, AM=5k

⇒AM=

51-50

step-by-step explanation: