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

Step-by-step explanation:

It is given that AC:CM = 3:4.

Therefore, let AC = 3k and CM = 4k

It is given that Δ ACM is right angled.

Therefore,

AM = 5k

But, AM = MP + AP

Therefore, MP + AP = 5k --- (1)

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

Multiply (1) and (2), we get.

(MP + AP)(MP - AP) = 5k × 1 = 5k

Add and subtract on the left side.

--- (3)

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

and

Now, (3) becomes,

7k = 5 or

AM = 5k

m

Step-by-step explanation: